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Black Holes Workshop XIII Program

 

21 December 2020, Monday
Session 0WelcomeChair: Organizing Committee
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09:00 - 09:30 Organizing Committee: Opening session and guidelines
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Session 1Nobel 2020Chairperson: José P. S. Lemos
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09:30 - 09:42
I will briefly review Penrose's singularity theorem, for which he was awarded the 2020 Physics Nobel Prize, and the role that this theorem played in the establishment of the modern picture of black hole formation.

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09:42 - 09:54
We will present the experimental component of this year's Nobel prize and the current status of the GRAVITY experiment. The experimental component was awarded to the leaders of the US and European groups working on the Galactic Centre supermassive black hole observations. The measurements conducting to the Nobel results have a timescale of decades. The most recent measurements have exquisite accuracy, in particular those from the GRAVITY experiment. This is not surprising because GRAVITY is the most advanced optical-infrared instrument in a ground-based observatory. It sharpens the light of four giant 8 m telescopes with advanced adaptive optics and them combines it interferometrically achieving such an exquisite precision. We will also present recent results from GRAVITY the collaboration, the most striking being the detection of ‎Schwarzschild precession in S2 star. Collaborators: Gravity Collaboration

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Session 2Scalar and vector fieldsChairperson: Miguel Zilhao
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09:54 - 10:06
Certain scalar-tensor theories of gravity provide negative-energy, tachyonic modes to a fundamental scalar inside matter, giving rise to non-perturbative phenomena around compact stars. Studies of this and other tachyonic instabilities always average over local matter properties. We use elementary, flat space models to understand possible collective effects and the accuracy of the averagingprocedure. In particular, we consider bodies made of elementary constituents which do not, inisolation, scalarize because their compactness is too small. We show that when the individual constituents have compactness smaller but close to the threshold, one is able to scalarizecomposite bodies through collective effects, and the compactness of the composite body can be madearbitrarily small. On the other hand, our results suggest that when the fundamental building blocks have very low compactness, then scalarization of the composite body requires a minimum global compactness. Thus, our results rule out scalarization of dilute bodies via collective effects. Collaborators: A. Foschi, M. Zilhão

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10:06 - 10:18
The detections of gravitational waves are opening a new window to the Universe. The nature of black holes and neutron stars may now be unveiled, but gravitational radiation may also lead to exciting discoveries of new exotic compact objects, oblivious to electromagnetic waves. In particular, Advanced LIGO-Virgo recently reported a short gravitational-wave signal (GW190521) interpreted as a quasi-circular merger of black holes, one at least populating the pair-instability supernova gap. We found that GW190521 is also consistent with numerically simulated signals from head-on collisions of two (equal mass and spin) horizonless vector boson stars (aka Proca stars). This provides the first demonstration of close degeneracy between these two theoretical models, for a real gravitational-wave event. Collaborators: Juan Calderon-Bustillo, José A. Font, Alejandro Torres-Forné, Avi Vajpeyi, Rory Smith, Carlos Herdeiro, Eugen Radu, Samson H. W. Leong

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10:18 - 10:30
Spontaneous scalarization of relativistic stars is one of the intriguing phenomena to test modified theories of gravitation with future strong gravity measurements. In this presentation, we are going to extend spontaneous scalarization to the higher spin sectors, namely, vector and spinor fields, and argue the properties and implications of vectorized and spinorized relativistic stars.

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10:30 - 10:42
We show that light scalars can form quasi-bound states around binaries. In the non-relativistic regime, these states are formally described by the quantum-mechanical Schr ̈odinger equation for a one-electron heteronuclear diatomic molecule. We performed extensive numerical simulations of scalar fields around black hole binaries showing that a scalar structure condensates around the binary – we dub these states “gravitational molecules”. We further show that these are well-described by the perturbative, non-relativistic description. Collaborators: Laura Bernard, Vitor Cardoso, Miguel Zilhao

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10:42 - 10:54
We construct and study rotating axion boson stars (RABSs). These are the spinning generalisations of the spherical gravitating solitons recently introduced in arXiv:1909.05515. RABSs are asymptotically flat, stationary, axially symmetric, everywhere regular solutions of the Einstein-Klein-Gordon theory, in the presence of a periodic scalar potential arising in models of axion-like particles. The potential is characterised by two parameters: the mass of the scalar field ma and the decay constant fa. We present an overview of the solution space, for different values of fa, and analyse some of their phenomenological properties. For large decay constants the solutions become identical to the standard spinning mini boson stars. For small decay constants, on the other hand, the solutions develop distinctive features. In particular, we analyse their compactness, the emergence of ergoregions, light rings and the distribution of stable and unstable equatorial timelike circular orbits, including the innermost stable circular orbit. We also establish the occurrence of violations of the strong energy condition for physical observers, for some RABSs. We observe some analogy between RABSs and spinning gravitating Q-balls. Collaborators: Carlos A. R. Herdeiro; Eugen Radu

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10:54 - 11:06
Spinning bosonic stars (SBSs) can form from the gravitational collapse of a dilute cloud of scalar/Proca particles with non-zero angular momentum. In a recent work we found that the scalar stars are transient due to a non-axisymmetric instability which triggers the loss of angular momentum. We further study the dynamical formation of SBSs using 3-dimensional numerical-relativity simulations of the Einstein-(massive, complex)Klein-Gordon system and of the Einstein-(complex)Proca system. We incorporate a quartic self-interaction potential in the scalar case to gauge its effect on the instability; we investigate (m=2) Proca stars to assess their stability; we attempt to relate the instability of SBSs to the growth rate of azimuthal density modes and the existence of a corotation point. We show that: the self-interaction potential can only delay the instability in scalar SBSs; m=2 Proca stars always migrate to the stable m=1 spheroidal family; unstable m=2 Proca stars and m=1 scalar boson stars exhibit a corotation point. This establishes a parallelism with rotating neutron stars affected by dynamical bar-mode instabilities. We compute the gravitational waves (GWs) emitted and investigate the detectability of the waveforms comparing the characteristic strain of the signal with the sensitivity curves of a variety of detectors, computing the signal-to-noise ratio. By assuming that the characteristic damping timescale of the bar-like deformation in SBSs is only set by GWs emission and not by viscosity (unlike in neutron stars), we find that the post-collapse emission could be orders of magnitude more energetic than that of the bar-mode instability itself. Our results indicate that GW observations of SBSs might be within the reach of future experiments, offering a potential means to establish the existence of such stars and to place tight constraints on the mass of the bosonic particle. Collaborators: Nicolas Sanchis-Gual, Pablo Cerdá-Durán, Miguel Zilhão, Carlos Herdeiro, José A. Font, Eugen Radu

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11:06 - 11:18
We show, by explicitly constructing the fully non-linear solutions, that static boson stars, composed of a single complex scalar field, can have a non-trivial multipolar structure, yielding the same morphologies for their energy density as those that elementary hydrogen atomic orbitals have for their probability density. This includes static configurations without any continuous symmetries. Axially symmetric boson star chains, with several distinct components located on the symmetry axis, are also discussed. Collaborators: C. Herdeiro, J. Kunz, I. Perapechka, Y. Shnir

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11:18 - 11:30
Recent studies have made key progress on the black hole/solitonic solutions of the Einstein-Proca system. Firstly, fully non-linear dynamical evolutions of the Kerr black hole superradiant instability, triggered by a Proca field, have shown the formation of a new equilibrium state, a spinning black hole with synchronised Proca hair. Secondly, non-linear evolutions of spinning Proca stars have established that they are dynamically stable, unlike their scalar cousins. Thirdy, separability of the Proca equation on the Kerr background has been achieved. Motivated by these results, we reconsider Kerr black holes with synchronised Proca hair. The separability of the Proca equation on the Kerr background allows us to examine the stationary Proca clouds in greater detail, in particular their dependence on the different quantum numbers. These stationary clouds occur at a set of existence lines in the Kerr parameter space, from which the black holes with synchronised Proca hair bifurcate. We construct the domain of existence of these black holes, comparing the fundamental states missed in the original study with the first excited states and with the cousin scalar model, giving illustrative examples of Kerr-like and non-Kerr-like BHs. Collaborators: Carolina L. Benone, Luís C. B. Crispino, Carlos A. R. Herdeiro, Eugen Radu

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11:30 - 11:42
In this work, we generalise the spontaneous scalarisation phenomena of Einstein-Maxwell-scalar models to a higher spin field. We develop and study a model wherein a vector field is non-minimally coupled to the Maxwell invariant by an exponential coupling function, an Einstein-Maxwell-Proca (EMP) model. Different than its scalar counterpart, the new \textit{spontanously vectorised} Reissner-Nordstr\"om (RN) black holes are always undercharged while being entropically preferable. A study of the solution profile, together with the entropical preference of the solutions in comparison with an equivalent RN black hole is performed, as well as a study on the possible astrophysical observational differences between the two solutions. Collaborators: J. Oliveira

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11:42 - 11:54
I will present our latest results regarding spontaneous scalarization in scalar-tensor theories that feature a coupling of the scalar field to the Gauss-Bonnet invariant. I will report on tachyonic instabilities that we observe in numerical simulations of linear scalar perturbations about Kerr black holes in this setup, and show how they appear only above a critical value of the spin parameter. I will eventually argue that the onset of these instabilities signals the existence of black hole solutions with scalar hair. Collaborators: Enrico Barausse, Nicola Franchini, Thomas Sotiriou

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11:54 - 12:06
I will present extreme mass ratio inspirals (EMRIs), during which a small body spirals into a supermassive black hole, in gravity theories with additional scalar fields. No-hair theorems and properties of known theories that manage to circumvent them introduce a drastic simplification to the problem: the effects of the scalar on supermassive black holes, if any, are mostly negligible for EMRIs in vast classes of theories. I will show how to exploit this simplification to model the inspiral perturbatively and demonstrate that the scalar charge of the small body leaves a significant imprint on gravitational wave emission. This result is particularly appealing, as this imprint is observable with LISA, rendering EMRIs promising probes of scalar fields.

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12:06 - 12:18
General Relativity (GR) is an extremely successful description of the gravitational interaction at different scales. One of its most dazzling and profound consequences is that gravitational collapse of massive stars gives rise to black holes. These are ubiquitous objects in our universe, and are now routinely observed and studied in the gravitational-wave band (currently the LIGO/Virgo constellation) but also in the electromagnetic band (with the GRAVITY instrument, the Event Horizon telescope and X-ray telescopes). To study black holes and test the underlying theory of gravity, a precise and complete knowledge of their dynamics is required, in addition to a knowledge of how matter behaves in curved spacetime. In the thesis, we focus on scalar and vector fields around spinning black holes. We present new results concerning massive vector fields in the vicinities of Schwarzschild-anti-de Sitter black holes. In particular, we provide a first principle analysis of vector fields in these geometries, using both a vector spherical harmonics decomposition and one recent ansatz to separate the relevant equations in spinning geometries, the Frolov-Krtouš-Kubizňák-Santos (FKKS) ansatz. We show that the FKKS ansatz is able to describe two polarizations: the longitudinal and the transversal polarization described by the electric modes. The quasinormal modes of such black holes and fields are calculated for both approaches in the non-rotating limit, providing further support to our results. Collaborators: Vítor Cardoso

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12:18 - 12:30
If ultralight bosonic fields exist in Nature as dark matter, superradiance spins down rotating black holes(BHs), dynamically endowing them with equilibrium bosonic clouds, here dubbed synchronised gravitational atoms(SGAs). The self-gravity of these same fields, on the other hand, can lump them into (scalar or vector) horizonless solitons known as bosonic stars (BSs). We show that the dynamics of BSs yields a new channel forming SGAs. We study BS binaries that merge to form spinning BHs. After horizon formation, the BH spins up by accreting the bosonic field, but a remnant lingers around the horizon. If just enough angular momentum is present, the BH spin up stalls precisely as the remnant becomes a SGA. Different initial data lead to SGAs with different quantum numbers. Thus, SGAs may form both from superradiance-driven BH spin down and accretion-driven BH spin up. The latter process, moreover, can result in heavier SGAs than those obtained from the former: in one example herein,∼18%of the final system’s energy and∼50% of its angular momentum remain in the SGA. We suggest that even higher values may occur in systems where in both accretion and superradiance contribute to the SGA formation.

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12:30 - 14:30 Lunch
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Session 3Numerical relativityChairperson: Eugene Radu
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14:30 - 14:42
The gauge-gravity duality, also known as holography, has established itself as a powerful tool for studying strongly coupled field theories. "Numerical holography" typically refers to the numerical solving of gravitational dynamics in asymptotically AdS geometries, allowing for the study of the far-from-equilibrium dynamics of such strongly coupled field theories. Applications range from studies of the applicability of hydrodynamics and computation of transport coefficients, to the dynamics of phase transitions. We introduce a new 3+1 evolution code called Jecco that solves the Einstein equations in the characteristic formulation in asymptotically AdS spaces. Jecco is written in the Julia programming language and is freely available. We present an outline of the code, its general features, and the tests performed to assess its robustness and performance, and some physical applications. Collaborators: Yago Bea, Thanasis Giannakopoulos, Aron Jansen, Mikel Sanchez-Garitaonandia

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14:42 - 14:54
Black hole excision is a method used in numerical relativity to remove the interior region of a black hole from the computational domain. In my talk I will present ongoing work in collaboration with Maitraya Bhattacharrya in which we are developing a new method for excision. The key idea is to use a "dual-frame" formulation of GR in generalized harmonic gauge to ensure both that the apparent horizon remains in the computational domain, and that the excision boundary itself remains outflow.

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14:54 - 15:06
I will describe a formalism to compute the second order gravitational (vacuum) perturbations of Kerr black holes, a numerical code that implements that formalism, and example output from the code. To motivate this work, I will discuss several applications where going beyond linear perturbation theory may be necessary, including modeling the “ringdown” of (near extremal) Kerr black holes, and modeling “black hole turbulence”. I will finish with directions for future work. Collaborators: Nicholas Loutrel, Elena Giorgi, Frans Pretorius

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Session 4Perturbation theoryChairperson: Vitor Cardoso
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15:06 - 15:18
Tidal perturbations play an important role in the study of the dynamics in the classical two-body system. We investigated how these kind of perturbations influence the geodesic motion when the system is composed by a Schwarzschild black hole and a companion with mass M_c. When the companion is steady at the pole it is possible to analitically obtain the radial potential and compute the Quasi Normal Modes spectrum in the eikonal limit. However, if the companion is located at the equator there is an axial symmetry breaking. We showed that timelike orbits experience a precession of the periastron while we numerically and analitically proved that closed elliptical null geodesic can still exist. In addition, we considered the companion to be in orbital motion with frequency Omega around the black hole and we showed the existence of corotating timelike orbits. Collaborators: Vitor Cardoso

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15:18 - 15:30
Scalar fields can give rise to confined structures, such as boson stars or Q-balls. These objects are interesting hypothetical new "dark matter stars", but also good descriptions of dark matter halos when the fields are ultralight. Here, we study the dynamical response of such confined bosonic structures when excited by external matter (stars, planets or black holes) in their vicinities. Such perturbers can either be plunging through the bosonic configuration or undergoing periodic motion around its center. Our setup can also efficiently describe the interaction between a moving, massive black hole and the surrounding environment. It also depicts dark matter depletion as a reaction to an inspiralling binary within the halo. We calculate total energy loss, and linear and angular momenta radiated during these processes, and perform the first self-consistent calculation of dynamical friction acting on moving bodies in these backgrounds. We show that the gravitational collapse to a supermassive black hole at the center of a Newtonian boson star (NBS) is accompanied by a small change in the surrounding core. The NBS eventually gets accreted, but only on times larger than a Hubble scale for astrophysical parameters. Stellar or supermassive binaries are able to "stir" the NBS and lead to scalar radiation. For binaries in the LIGO or LISA band, close to coalescence, scalar emission affects the waveform at leading -6 PN order with respect to the dominant quadrupolar term; the coefficient is too small to allow detection by next-generation interferometers. Our results provide a complete picture of the interaction between black holes or stars and the ultralight dark matter environment they live in. Collaborators: Lorenzo Annulli, Vitor Cardoso

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15:30 - 15:42
One pressing issue in GW physics regards the understanding of the signatures of matter in the near-horizon region. How to estimate these imprints on the GW spectrum can be an arduous task for numerical relativists. However, there exists an approximated but very powerful perturbative method to find the ringdown waveforms and the modes produced by the coalescence of black hole binaries in General Relativity. This is called the Close Limit Approximation of black holes (CLAP). In this talk I want to show how to expand the validity of CLAP to different, non standard, scenarios. As an example, we can use CLAP in alternative theories or in GR in the presence of extra fields (Reissner Nordstrom spacetimes, for instance). Finally I want to use CLAP as a technical apparatus to investigate the excitations of black hole mimickers, therefore to study the post-merger phase of the coalescence between compact but horizonless bodies.

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15:42 - 15:54
During its third observation run, the LIGO-Virgo collaboration detected three binary black-hole (BH) coalescences unlikely to be composed by two first-generation BHs. Instead, the latter should be remnants of previous mergers, and a third-body, e.g. a supermassive BH, should be present to induce their coalescence. In this talk, we will discuss how these so-called hierarchical triple mergers can be understood as an extreme-mass-ratio inspiral problem where a "small" binary orbits a supermassive BH. We will show that the binary is able to excite the quasinormal modes of the third-body, in analogy with the resonant excitation of two tuning forks with the same proper frequency. Finally, we will discuss possible gravitational wave signatures of these systems and their astrophysical relevance to the upcoming LISA mission. Collaborators: Vitor Cardoso, Gaurav Khanna

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15:54 - 16:06
Gravitational-wave astronomy, together with precise pulsar timing and long baseline interferometry, is changing our ability to perform tests of fundamental physics with astrophysical observations. Some of these tests are based on electromagnetic probes or electrically charged bodies, and assume an empty universe. However, the cosmos is filled with plasma, a dilute medium which prevents the propagation of low-frequency, small-amplitude electromagnetic waves. We show that the plasma hinders our ability to perform some strong-field gravity tests, in particular: (i) nonlinear plasma effects dramatically quench plasma-driven superradiant instabilities; (ii) the contribution of electromagnetic emission to the inspiral of charged black hole binaries is strongly suppressed; (iii) electromagnetic-driven secondary modes, although present in the spectrum of charged black holes, are excited to negligible amplitude in the gravitational-wave ringdown signal. Collaborators: Vitor Cardoso, Caio F. B. Macedo, Paolo Pani

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Session 5LensingChairperson: João Costa
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16:06 - 16:18
The ringdown and shadow of the astrophysically significant Kerr Black Hole (BH) are both intimately connected to a special set of bound null orbits known as Light Rings (LRs). Does it hold that a generic equilibrium BH must possess such orbits? In this work we prove the following theorem: a stationary, axi-symmetric, asymptotically flat black hole spacetime in 1+3 dimensions, with a non-extremal, topologically spherical, Killing horizon admits, at least, one standard LR outside the horizon for each rotation sense. The proof relies on a topological argument and assumes C2-smoothness and circularity, but makes no use of the field equations. The argument is also adapted to recover a previous theorem establishing that a horizonless ultra-compact object must admit an even number of non-degenerate LRs, one of which is stable. Collaborators: Carlos A.R. Herdeiro

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16:18 - 16:30
In this talk I present two recent works that either use black hole quasi-normal modes [1] or the black hole shadow-size [2] to constrain the underlying metric of the space-time. Both types of observations are accessible by current and future activities of the LIGO/Virgo/KAGRA gravitational wave detectors or the Event Horizon Telescope. By combining Bayesian analysis with parametrized black hole metrics it is possible to approximate the underlying black hole space-time and solve the inverse problem, under some simplifying assumptions that will be outlined. I will discuss opportunities, limitations and moreover, how both types of observations are complementary to each other. [1] S. H. Völkel, E. Barausse, Phys. Rev. D 102, 084025, 2020, https://arxiv.org/abs/2007.02986. Collaborators: Barausse, Franchini, Broderick

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16:30 - 16:42
One of the consequences of Einstein’s general theory of relativity is bending of light as it passes through a gravitational field. Examining the path of light in a very strong gravitational field of a black hole can provide a huge amount of information about the geometry and characteristics of the surrounding space. On the other hand, the path of light rays, extent, and shape of gravitational lensing, are directly related to the type of background geometry in which light is emitted. Since the theory of general relativity in very high energies and very strong gravitational fields is expected to be corrected, researchers have been looking at the phenomenon of gravitational lensing in the context of alternative theories for general relativity to find out the needed corrections for the results of general relativity and these corrections are likely to be more significant in a very strong gravitational field of a black hole. Among the various theories that have been proposed for correcting the gravity in high energies, gauge theories of gravity have great importance. One of the important results of these theories is changing the geometry for the background in general relativity, Riemannian space-time, to a non-Riemannian geometry in which, in addition to curvature, there is also torsion. In these theories, the presence of torsion coupled to the spin of a matter can affect the path of light rays and correct the results of gravitational lensing. In this work, we want to study the effects of non-Riemannian geometry on the gravitational lensing of a black hole, and in particular the effects of torsion and spin in this context. Collaborators: Siamak Akhshabi

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General Assembly of SPRG
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16:42 - 17:30 General Assembly of the Portuguese Society of Relativity and Gravitation for members
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22 December 2020, Tuesday
Session 6Higher dimensions, semiclassical gravity, string theoryChairperson: David Hilditch
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09:30 - 09:42
We study the thermodynamics of Schwarzschild-Tangherlini black holes in the canonical ensemble in any dimension d. This generalizes the approach developed by York for the 4 dimensional Schwarzschild black hole, and highlights the importance of the roles of two regions of the spacetime on the thermodynamic properties of black holes: the photon sphere, and the Buchdahl limit. These play an important role in the black hole's thermodynamic stability, and the black hole's ability to transition to hot flat space. Collaborators: José P. S. Lemos.

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09:42 - 09:54
Consider the question: should a detector click more when surrounded by a hotter thermal bath? Turns out the answer to this question depends on the dimension of the spacetime, and on the quantum state the detector is interacting with. When the response of a detector measuring Hawking radiation decreases with respect to the local Hawking temperature, we say the anti-Hawking effect is manifest and the answer to the question is simply "no". In this talk, I approach this question considering an Unruh-DeWitt detector following static trajectories and coupled for an infinite proper time interval to both a ground state and to a KMS state on massless topological black holes. The answer I shall give is as in the work entitled "Ground and thermal states for the Klein-Gordon field on a massless hyperbolic black hole with applications to the anti-Hawking effect. Collaborators: Claudio Dappiaggi.

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09:54 - 10:06
We compute the Renormalized Stress-Energy Tensor (RSET) of a massless minimally coupled scalar field in the Regularized Polyakov approximation, as well as its backreaction, on the classical Reissner-Nordström spacetime. The complete set of solutions of the semiclassical equations is obtained and compared with the classical counterparts. The semiclassical Reissner-Nordström family involves three kinds of geometries that depend on the charge-to-mass ratio of the spacetime. In the under-charged regime, the geometry has its external horizon replaced by a wormhole neck that leads to a singular asymptotic region at finite proper distance. The over-charged regime reveals a naked singularity coated by a cloud of (infinite) mass coming from the quantized field. In between both behaviours there is a separatrix solution that smoothly connects to the extremal Reissner-Nordström geometry in the classical limit. As the RSET over an extremal horizon is finite, the semiclassical backreaction does not get rid of the horizon. Nonetheless, we show that the resulting horizon is no longer extremal. Collaborators: Carlos Barceló, Raúl Carballo-Rubio, Luis J. Garay.

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10:06 - 10:18
We analyse the backreaction of a quantum field on a spherically symmetric black hole geometry with an inner horizon, i.e. an internal boundary of the trapped region. We start with a black hole background with an inner horizon which remains static after its formation. We quantise a massless scalar field on it and calculate its renormalised stress-energy tensor in the Polyakov approximation. We use this tensor as a source of perturbation on top of the background spacetime. We find that the inner horizon has a tendency to evaporate outward much more quickly than the outer one evaporates inward through the Hawking effect. This suggests a revised picture of a semiclassically self-consistent evaporation in which the dominant dynamical effect comes from the inner horizon. We also look at backreaction on backgrounds which resemble gravitational collapse, where the inner horizon moves toward the origin. There we find that, depending on the nature of the background dynamics, horizon-related semiclassical effects can become dominant and invert the collapse. Collaborators: Carlos Barceló, Raúl Carballo-Rubio, Luis J. Garay.

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10:18 - 10:30
I will discuss the recent calculation (arXiv:2007.06582) of the leading α′ corrections to the entropy of certain black holes with AdS5×S5 asymptotics, namely in the supersymmetric limit, the entropy does not receive α′ corrections. This result strengthens recent calculations that match the index of N=4 Super-Yang-Mills with the corresponding partition function in the supersymmetric limit. In the small temperature regime, the entropy corrections are concordant with the weak gravity conjecture. Collaborators: Jorge E. Santos.

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10:30 - 10:42
In this work, we compute analytical expressions for quasinormal frequencies, associated with tensor type gravitational perturbations and complex massless scalar field perturbations, in the string corrected d-dimensional Callan Myers Perry black hole space time. We do this for two distinct limits. First, we compute these frequencies in the eikonal limit, resorting to WKB approximations. We then compute these frequencies in the asymptotic limit, studying two different monodromies of the perturbation, when analytically continued to the complex r-plane. Collaborators: Filipe Moura.

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Session 7Alternative gravityChairperson: Justin Feng
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10:42 - 10:54
Finite-sized bodies are deformed in the presence of external tidal fields created, for instance, by surrounding objects. This is particularly important in the merging process of black holes or neutron stars, whereby the phase of the gravitational waveform produced is affected by such tidal Love numbers. This idea has been used to constrain the nuclear matter equation of state from the gravitational wave detection of binary neutron star mergers. It is a well known fact that non-rotating black holes in General Relativity (GR) have vanishing Love numbers. Nevertheless, this exact same spacetime is also a solution of a broad class of modified gravity theories, for which the linearized perturbations equations generically differ from those of GR. A direct consequence is that the tidal Love numbers depend not only on the object itself, but also on the gravitational theory supporting it, offering the possibility of ruling out theories with detections of gravitational waves from binary black hole mergers. I will discuss linear perturbations of f(R) gravity on the background of a Schwarzschild-AdS black hole, and determine the associated tidal Love numbers. While axial sector perturbations remain unaltered with respect to GR --and therefore the axial Love numbers vanish in the absence of a cosmological constant--, the polar sector is affected. Results for two cases of particular relevance will be highlighted: (i) the Schwarzschild spacetime, regarded as a solution in f(R) gravity, and (ii) the Schwarzschild-AdS solution in GR. Collaborators: Edgardo Franzin.

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10:54 - 11:06
We propose a regularization procedure for the Einstein-Gauss-Bonnet theory in 4D. Our method is conceptually similar to the dimensional regularization procedure used in quantum field theories and results in a generalized scalar-tensor theory that shares many features with its higher-dimensional counterpart. Exact black hole solutions in closed-form are discussed, along with observational constraints on the theory.

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11:06 - 11:18
Spherically symmetric black hole's solution with nonabelian gauge field is derived in the theory with nonminimal derivative coupling (Horndeski gravity). The obtained solution is studied and compared with corresponding solutions in Einsteinian General Relativity. Some aspects of thermodynamics are also examined.

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Session 8Various topicsChairperson: José Natário
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11:18 - 11:30
If two particles collide in a strong gravitational field, their energy E_cm in the center of mass frame can become unbounded under certain conditions. This includes collisions near black holes, naked singularities, rotating wormholes. In the present talk, we discuss new possibilities which extend the general scheme. (i) High-energy particle collisions when both particles move under the action of finite force. We show that in this case, unbounded E_cm are possible even for the Schwarzschild metric. (ii) Special scenario that includes particles with almost zero-energy. We show that for free particles, unbounded E_cm are absent in the Schwarzschild metric. However, for the Reissner-Nordstrom one, collision of pure neutral particles does lead to unbounded E_cm.

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11:30 - 11:42
Electromagnetic duality is discussed in the context of Einstein-Maxwell-scalar (EMS) models including axionic-type couplings. This family of models introduces two non-minimal coupling functions f(ϕ) and g(ϕ), depending on a real scalar field ϕ. Interpreting the scalar field as a medium, one naturally defines constitutive relations as in relativistic non-linear electrodynamics. Requiring these constitutive relations to be invariant under the SO(2) electromagnetic duality rotations of Maxwell's theory, defines 1-parameter, closed duality orbits in the space of EMS models, connecting different electromagnetic fields in "dual" models with different coupling functions, but leaving both the scalar field and the spacetime geometry invariant. This mapping works as a solution generating technique, extending any given solution of a specific model to a (different) solution for any of the dual models along the whole duality orbit. We illustrate this technique by considering the dual. Collaborators: Carlos A. R. Herdeiro.

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11:42 - 11:54
Carter-Penrose diagrams are a very useful tool to describe and understand the causal properties of spacetimes. In the context of numerical relativity, I will consider spherically symmetric simulations on hyperboloidal slices. The latter are of special interest because they reach future null infinity, formed by the endpoints of future-directed null geodesics and where global quantities of spacetimes are unambiguously defined. More specifically, the focus will be on the evolution of initial constant-mean-curvature hyperboloidal trumpet slices of the Schwarzschild spacetime for some suitable gauge conditions in vacuum. I will describe the construction of Penrose diagrams for the numerical slices and show results for the case where the trumpets have relaxed to a stable stationary endstate. Progress on how to tackle the representation of slicings in the dynamical regime will be reported on. Collaborators: David Hilditch.

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11:54 - 12:06
Entropy and energy are found to be closely tied on our quest for quantum gravity. We point out an interesting connection between the recently proposed outer entropy, a coarse-grained entropy defined for a compact spacetime domain motivated by the holographic duality, and the Bartnik-Bray quasilocal mass long known in the mathematics community. In both scenarios, one seeks an optimal spacetime fill-in of a given closed, connected, spacelike, codimension-two boundary. We show that for an outer-minimizing mean-convex surface, the Bartnik-Bray inner mass matches exactly with the irreducible mass corresponding to the outer entropy. The equivalence implies that the area laws derived from the outer entropy are mathematically equivalent as the monotonicity property of the quasilocal mass. It also gives rise to new bounds between entropy and the gravitational energy, which naturally gives the gravitational counterpart to Wall's ant conjecture. We also observe that the equality can b e achieved in a conformal flow of metrics, which is structurally similar to the Ceyhan-Faulkner proof of the ant conjecture. We compute the small sphere limit of the outer entropy and it is proportional to the bulk stress tensor as one would expect for a quasilocal mass.

12:06 - 12:18 Question time
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12:18 - 12:30 Free discussion
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12:30 - 14:30 Lunch
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Session 9Mathematical relativityChairperson: Pedro Cunha
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14:30 - 14:42
We will show the proofs of the Hawking-Penrose theorems in a sketchy way and will point out their importance in the development of black hole theory.

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14:42 - 14:54
The Teukolsky equation is one of the fundamental equations governing linear gravitational perturbations of this family, and has been the focus of intense study for over 50 years.

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14:54 - 15:06
In spherical symmetry compelling numerical evidence suggests that in general relativity solutions near the threshold of black hole formation exhibit critical behavior. One aspect of this is that threshold solutions themselves are self-similar and are, in a certain sense, unique. To an extent yet to be fully understood, the same phenomena persist beyond spherical symmetry. It is therefore desirable to construct models that exhibit such symmetry at the threshold of blow-up. Starting with deformations of the wave equation, we discuss models which have discretely self-similar threshold solutions. We study threshold solutions in the past light cone of the blow-up point. In spherical symmetry there is a sense in which a unique critical solution exists. Spherical numerical evolutions are also presented for more general models, and exhibit similar behavior. Away from spherical symmetry threshold solutions attain more freedom. Different topologies of blow-up are possible, and even l. Collaborators: Rodrigo Vicente, David Hilditch.

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15:06 - 15:18
In this talk, I will revise the infinite-dimensional symmetries that emerge in the near horizon region of black holes. I will show that, in the case of extremal horizons, this includes the Bondi–Metzner–Sachs (BMS) symmetries.

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15:18 - 15:30
The Bondi-Sachs formalism is crucial to the understanding of gravitational waves and underpins codes that aim to produce waveforms of high accuracy. The well posedness of the resulting system of partial differential equations is a necessary condition in order for the numerical approximation to converge to the continuum solution. Well posedness of the initial value problem in the L2 norm is characterized by strong hyperbolicity. I will describe a hyperbolicity analysis of the Bondi-Sachs system, which shows that this system is only weakly hyperbolic. Then, I will demonstrate the consequence of weak hyperbolicity in numerical experiments. Collaborators: David Hilditch, Miguel Zilhão.

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15:30 - 15:42
In this talk I will present a derivation that avoids the Raychaudhuri equation and instead makes use of index form methods. I will discuss how this is an improvement over existing methods and how it can be applied to prove theorems with weakened hypotheses. Then I will present derivations of semiclassical singularity theorems both in the timelike and the null case and discuss the challenges and open questions for each case.", within "The classical singularity theorems concern matter obeying the strong energy condition in the timelike case and the null energy condition in the null case. However, all quantum fields violate such pointwise energy conditions and thus, the realm of semiclassical gravity is outside the scope of these theorems. Therefore there is a need to develop theorems with weaker restrictions, namely quantum energy inequalities, weighted local averages of energy densities.

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15:42 - 15:54
I will review the motivations (from classical as well as quantum field theory) for studying electromagnetism and linearized gravity in harmonic gauge (locality and regularity, simplicity of residual gauge freedom, renormalization of interactions). Unfortunately, this choice of gauge leads to technical difficulties on non-flat backgrounds, like the Schwarzschild black hole, due to rather complicated radial mode equations, even after separation of variables. I will then describe a recent series of works, in which I have taken steps to overcome these difficulties by explicitly decoupling the radial mode equations into sparse triangular form.

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15:54 - 16:06
Recent work has argued that the strong cosmic censorship (SCC) conjecture is violated by near-extremal Reissner-Nordstrom de Sitter (RNdS) black holes but respected by Kerr-de Sitter black holes. It has also been shown that the conjecture is violated by near-extremal BTZ black holes. The latter result relies on a coincidence between ``exterior'' and ``interior'' quasinormal frequencies. If this coincidence were to occur also for RNdS or Kerr-dS then it would significantly modify the conclusions of earlier work. In this talk, I will prove that this coincidence does not occur for RNdS or Kerr-dS and so the conclusions of the earlier work remain valid.

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Session 10Exact solutionsChairperson: Ana Mourão
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16:06 - 16:18
In this talk, I discuss portal wormholes (also known as loop based thin shell wormholes or gates) supported by a single loop of negative mass (in a local sense) cosmic string. I consider a situation in which the portal mouths collide, which naively looks like a topology changing process. To determine whether gravity encourages or obstructs the collision, the smoothing of the cosmic string and the self interaction as the portal mouths are brought together are examined. Collaborators: José P. S. Lemos and Richard A. Matzner.

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16:18 - 16:30
We propose two models for constant density relativistic perfect-fluid spheres supported by thin shell configurations. These models are obtained from the Schwarzschild constant density star solution: the first via the collapse of the external layers of the fluid into a thin shell by performing a matching with the exterior Schwarzschild solution at a matching radius smaller than the star radius; and the second via the creation of a vacuum bubble inside the star by matching it with an interior Minkowski spacetime. Both models are shown to satisfy both the weak and the strong energy conditions (WEC and SEC) and can have a compactness arbitrarily close to that of a black-hole without developing singularities at the center, thus being exceptions to the Buchdahl limit. We compute the stability regimes of the models proposed and we show that there are combinations of the star radius R and the matching radius R_Sigma for which the solutions are stable, the dominant energy condition (DEC) is satisfied, and the radius of the object is smaller than $3M$, implying that these models could be used as models for dark matter or exotic compact objects. Collaborators: Pedro Piçarra.

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16:30 - 16:42
The simplest Weyl-class solution of the Einstein equations is the single Curzon-Chazy particle, well known for its direction-dependent singularity.By adding phantom scalar field as a source we can obtain a new solution which is spherically symmetric. This solution resembles a spherical wormhole and is completely devoid of curvature singularities, nevertheless it still retains some singular properties.

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16:42 - 16:54
The classical spacetime is usually described by a differentiable manifold with infinitely many degrees of freedom. Occasionally though, it is useful to consider an approximation whose number of degrees of freedom is finite. There are several discrete models of spacetime like that, some of which have been used to build a (simplified) representation of a black hole. We will shortly revisit these discrete black hole models. Then we limit ourselves to one particular case and show how it can be inhabited by quantum matter fields. It is suggested that the field dynamics should be described by the framework of non-unitary discrete linear evolution, and we point out some of the most significant implications of this approach.

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16:54 - 17:06
The general parametrization of a black-hole spacetime in arbitrary metric theories of gravity includes an infinite set of parameters. It is natural to suppose that essential astrophysically observable quantities, such as quasinormal modes, parameters of shadow, electromagnetic radiation and accreting matter in the vicinity of a black hole, must depend mostly on a few of these parameters. Starting from the parametrization for spherically symmetric configurations in the form of infinite continued fraction, we suggest a compact representation of the asymptotically flat spherically symmetric and slowly rotating black holes in terms of only three and four parameters respectively. A subclass of arbitrarily rotating black holes belonging to the Carter family can also be parametrized by only four parameters. This approximate representation of a black-hole metric should allow one to describe physical observables in the region of strong gravity.

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17:06 - 17:18
A new coordinate system that goes from the Painlevé-Gullstrand partial extension to the Kruskal-Szekeres maximal extension of the Schwarzschild metric is found, thus unifying in a single picture several different coordinate systems. This is performed by using two time coordinates, one is the proper time of a congruence of outgoing timelike geodesics, the other is the proper time of a congruence of ingoing timelike geodesics, both parameterized by the same energy per unit mass E. Our family of extensions is different from the Novikov-Lemaitre family parameterized also by the energy E of timelike geodesics, with the Novikov extension holding for 0<E<1 and being maximal, and the Lemaitre extension holding for 1 leq E < infty and being partial, not maximal, and moreover its E=infty limit evanescing in a Minkowski or in a Kasner spacetime rather than ending in the Kruskal-Szekeres spacetime. In addition, a revision of the Synge-Fronsdal-Kruskal-Szekeres maximal analytic extension in Kruskal-Szekeres coordinates with some of the historic highlights will be given. Collaborators: Diogo Silva.

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Session 11Round table with the participantsChairperson: Carlos Herdeiro
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17:18 - 17:30


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