I have a broad range of interests. My research topics over the past years include cosmic strings, information paradox, gauge/gravity dualities, fluid lump solutions dual to black holes, integrability in (super)gravity and cosmic censorship. (Click on each topic to expand/collapse.)
Cosmic strings
Cosmic strings are cosmologically viable topological defects that might arise in the universe when phase transitions occur as a consequence of spontaneous symmetry breaking. These objects were first proposed by Kibble in the late 70's. At the beginning of the millennium, it was realized that such defects could also be embedded in string theory, in which case they were dubbed 'cosmic superstrings'. This possibility led to a renewal of interest in the field.
The presence of cosmic strings populating our universe can, in principle, be detected. In fact, their existence would lead to several observable effects, including imprints in the Cosmic Microwave Background, characteristic gravitational lensing and generation of gravitational waves. The existence of cosmic strings has not been observationally confirmed yet. Nevertheless, the detection of such remnants should give us valuable information about the early universe, such as the symmetry breaking scale that originated the cosmic strings.
The evolution of cosmic string networks in expanding spacetimes is a notoriously difficult problem. However, it is important to understand the dynamics of these networks as this will allow us to better place constraints on the physical parameters of the defects and of the theory that harbors them. Such understanding will also provide a guide for searches of cosmic strings in the sky. Last, but not least, if one day cosmic strings are discovered we need to know how to interpret the data.
The large scale (i.e., scales comparable to the cosmological horizon) properties of cosmic string networks have been understood long ago, in the late 80's, via numerical simulations. It turned out that, irrespective of the initial distribution, the latetime configuration of the network always approaches the socalled 'scaling regime', in which all length scales grow proportionally with time. The situation with the small scale structure, which was observed already in the early simulations, was much less clear and remained an issue of debate for a long time (and in some aspects, still does!). Does the small scale structure also approach a scaling regime? Is gravitational radiation necessary for that? What is the typical scale of cosmic string loops?
The above questions are very hard to address entirely with numerical methods, given the large ratios of length and time scales involved. On the other hand, analytic methods are difficult because of the highly nonlinear nature of the system. However, a combination of both has allowed us to make progress. The idea is to consider as a first approximation the dominant effects that determine the cosmic string evolution and later add the subdominant effects as small perturbations. The resulting model has a few undetermined parameters which are then fixed by comparison with the simulations. This was the approach followed by Joseph Polchinski and myself, which led us to propose a model for cosmic string networks evolution. In many aspects, this simple model yields a satisfactory comparison with the most recent simulations and it has been exploited in collaborations with Florian Dubath, as well as several other authors.
Information paradox and the AdS/CFT correspondence
The famous information loss problem was posed by Hawking in 1976 shortly after his revolutionary discovery that black holes radiate quantum mechanically. According to Hawking's original computation the emitted radiation distribution follows a featureless blackbody spectrum. It was soon realized that information seemed to be lost in the course of formation and consequent evaporation of black holes. This becomes evident when one considers the formation of a black hole by gravitational collapse of an initial matter distribution in a pure quantum state. Assuming a black hole does form and that it decays completely according to Hawking's law, the final state would be a thermal (i.e., maximally mixed) state, leading to an obvious violation of unitarity.
The AdS/CFT correspondence offers a new perspective on the longstanding information paradox. This powerful duality holographically relates gravitational dynamics in an antide Sitter (AdS) background with a (gravityfree!) conformal field theory living on the boundary of AdS. It has been pointed out since the early days of AdS/CFT that the manifest unitarity of the dual gauge theory should prevent any information loss from occurring. If so, we still need to understand where Hawking's argument, which originated the paradox, failed. To this end we can also employ the AdS/CFT correspondence to follow the evaporation process of a black hole from the field theory side.
Naturally, we should then consider a black hole in AdS. These objects come in two classes: small and large. Small AdS black holes are thermodynamically unstable and do not have a clear interpretation in terms of the dual CFT. On the other hand, large AdS black holes are thermodynamically stable. These objects are dual to a high temperature thermal state in the CFT. To make progress exploiting the AdS/CFT correspondence we should then consider a large black hole in AdS. However, as it stands there is a clear obstacle to the formulation of the information paradox using large AdS black holes: these objects are stable and they do not evaporate!
To address this issue I have developed a simple toy model (suggested to me by Joseph Polchinski) that allows large AdS black holes to decay, by coupling the emitted radiation to an external scalar field propagating in an auxiliary space. This effectively changes the properties of the boundary of AdS, making it partly absorbing. In this evaporon model one can demonstrate that the evaporation process never ceases by explicitly computing the transmission cofficient for a wave scattering from the bulk into auxiliary space and the greybody factor for a black 3brane (playing the role of a large black hole) in an AdS background. Therefore, this setting provides an simple testbed to address the information paradox using AdS/CFT techniques.
Lobed plasma balls and the fluidgravity correspondence
The idea of a connection between black holes and hydrodynamics dates back to the 1970’s. The picture that emerged from those days is commonly referred to as the 'membrane paradigm'. Recently this analogy has been promoted to a precise mapping between gravitational systems and fluid dynamics, due to a pathbreaking paper by Bhattacharyya, Hubeny, Minwalla and Rangamani. The resulting duality was dubbed the 'fluidgravity correspondence' and follows naturally from the AdS/CFT program and the observation that any interacting quantum field theory is effectively described by hydrodynamics at long wavelengths.
The rationale behind the fluidgravity correspondence is to perturb (in a very controled way) black hole solutions of EinsteinAdS gravity and perform a derivative expansion of the field equations. It turns out that requiring those to hold at each order of perturbation simply yields the equations of hydrodynamics for the boundary of AdS. Moreover, the duality also provides a onetoone map between the bulk gravity solution and the boundary system.
An interesting application of the fluidgravity correspondence concerns systems possessing a confinement/deconfinement transition. Such theories resemble more closely quantum chromodynamics (QCD) than the prototypical N=4 Super YangMills and one migth hope to learn about real world strong interactions through this duality. A simple realization of a system with a confinement/deconfinement transition is obtained by a ScherkSchwarz (SS) compactification (where one of the spatial dimensions is taken to be curled up into a small circle). On the other hand, studies using the dual hydrodynamic side indicate that black holes in SSAdS have surprising similarities with asymptotically flat black hole spacetimes.
Concretely, in the long wavelength regime, the SS compactification of a (d + 1)dimensional CFT has an effective description as a ddimensional fluid dynamics. This system is dual to the SS compactification of (d + 2)dimensional AdS gravity. The SS theory has both a confined and a deconfined phase. In the gravity side of the duality the deconfined phase corresponds to a black hole solution localized in the infrared region of the holographic direction, while the confined phase maps to the AdS soliton solution. They compete with each other to minimize the free energy. In the neighborhood of the confinement temperature the two phases coexist in different regions of the spacetime and are separated by a domain wall. In the holographic boundary where the fluid lives, the deconfined phase is described by a plasma lump immersed in the confined sea phase. The plasma lump has a surface tension at its boundary that is in correspondence with the domain wall tension in the bulk.
A few years ago it has been recognized that plasma balls and plasma rings correspond, respectively, to rotating black holes and black rings in SSAdS. These are axisymmetric solutions. However, rotating plasma balls were found to be unstable against mlobed perturbations. Starting with a static plasma ball and increasing its rotation, the axisymmetric rotating plasma ball becomes unstable first to a 2lobed (“peanutlike”) perturbation and then to mlobed perturbations with m > 2. Usually, such an instability signals a bifurcation point to a new branch of stationary solutions (that obeys the symmetries of the instability) in the phase diagram of stationary solutions.
In 2009 Vitor Cardoso, Óscar Dias and myself explicitly constructed the branch of 2lobed plasma balls in the phase diagram of solutions. More generally, we were able to find the nonaxisymmetric profile of mlobed plasmas, which should be in correspondence with (quasi)stationary nonaxisymmetric black holes in the dual gravitational theory. We also showed that the possibility of mlobed plasma rings is excluded, at least as a perturbations of axisymmetric plasma rings. Our findings point at the need of a better understanding of the fluidgravity correspondence and, in particular, of the dual of gravitational radiation as nonaxisymmetric rotating black holes are expected to emit gravitational waves.
Integrability of 5D minimal supergravity
The search for solutions of a given theory is greatly simplified by the assumption of symmetries. For (super)gravity theories in D dimensions, the presence of D2 commuting Killing symmetries originates a twodimensional nonlinear sigma model coupled to 2D dilaton gravity. It is well known that, even though highly interacting, these models are classically completely integrable. The integrability may be used as a solution generating technique but until very recently this had only been accomplished for vacuum gravity in various dimensions and EinsteinMaxwell theory.
For vacuum gravity, Belinsky and Zakharov presented in 1978 a systematic procedure for generating new solutions from previously known solutions. The prescription, reminiscent of the inverse scattering method for 2d chiral models, is applicable when the metric depends only on two variables. In recent years this line of investigation has led to great progress in five dimensional vacuum gravity regarding stationary black holes with two rotational Killing vectors. In particular, the inverse scattering technique has been employed to derive several new black ring solutions.
In 2009, a collaboration comprised by Pau Figueras, Ella Jamsin, Amitabh Virmani and myself has tackled the problem of exploring the integrability of fivedimensional minimal supergravity. The hope is that this will allow us to construct the most general black rings, possessing five parameters, that have been conjectured to exist, whereas the presently known regular solutions have three independent parameters at most.
Our efforts show that the BelinskyZakharov method generalizes to 5D minimal supergravity in almost all respects. Specifically, we obtained a Lax pair formulation of the nonlinear equations of motion based on a symmetric 7x7 representative matrix for the coset G2/SL(2,R)xSL(2,R). As an illustration of the formalism we obtained the doubly spinning 5D MyersPerry black hole by applying solitonic transformations on the Schwarzschild solution. In addition, intertwinning with the hidden symmetry transformations belonging to the coset group we easily derive the CveticYoum black hole from ReissnerNordstrom.
Higher dimensional black holes and cosmic censorship
The cosmic censorship conjecture states that, under generic conditions, naked singularities cannot be formed by gravitational collapse of regular initial data. Certainly singularities can be produced by the collapse of matter but it is firmly believed that they generically appear hidden behind the event horizon of a black hole.
Of course, solutions are known that contain naked singularities, the simplest of which is the overextreme Kerr solution in four spacetime dimensions. In fact, the angular momentum of Kerr black holes is bounded by the square of its mass. Thus, if it were possible for the black hole to capture particles of high enough angular momenta, then one might exceed this bound (i.e., overspin the black hole), possibly creating a naked singularity. In 1974, Wald showed this cannot happen, as the potentially dangerous particles are never captured by the black hole  a potential failure of the cosmic censorship is prevented.
In 2010, Mariam BouhmadiLópez, Vitor Cardoso, Andrea Nerozzi and myself considered extending Wald's analysis to other spacetimes, whose absence of naked singularities imposes some bounds on the angular momentum. In particular, we considered the MyersPerry (MP) family of rotating black holes in higher dimensions and the fivedimensional dipole black ring (including the neutral ring as a particular case). MP black holes with all angular momenta equal exhibit upper bounds on their spin. This is also true for the MP black hole in five dimensions rotating in a single plane but it doesn't generalize to higher dimensions. The case of the dipole ring possesses both lower and upper bounds on the angular momentum.
We found that the bounds on the spins of all black objects considered are always preserved in the process envisaged. A particularly interesting analytically tracktable case is the extremal 5d MP black hole with both spins equal. Throwing in a point particle along an equatorial plane can generate an angular momentum above the extremal bound (for equalrotation black holes) but the remaining rotation paramenter decreases in the process and the final configuration still lies on the curve of extremal fivedimensional MyersPerry solutions. It seems that black holes know when we are trying to trick them or at least that they are testparticleproof! These results obtained for pointparticles might be very useful to understand and guide numerical simulations of black hole collisions in four and higher dimensions, and indeed in the studies so far the formation of naked singularities was never observed.
We have also been able to extend the above program to the (2+1)dimensional black hole in AdS, the BañadosTeitelboimZanelli (BTZ) black hole, with similar results. The extension of the spinup analysis itself to AdS backgrounds does not offer any additional difficulty but there is one issue that must be addressed: how to pinpoint the conserved quantities "energy" and "angular momentum" of the test particles when the spacetime is not asymptotically flat? In order to answer this question we studied gravitational perturbations induced by a circular shell of test particles on the BTZ geometry. This particular setup is chosen so that the symmetry of the background is not spoiled, thus simplifying the technical analysis of the problem. The final result is that the correct conserved quantities are exactly what we would naivelly expect, i.e., they are given by the contraction of the velocity of the particle with the corresponding Killling vectors.
Constructing dipole black rings
The first examples of black rings carrying dipole charge were presented by Emparan in 2004. The main novelty of these solutions is that they are characterized not only by their conserved charges (mass, angular momentum) but also by a nonconserved dipole charge. Therefore, this amounts to an infinite nonuniqueness of black ring solutions if specified solely by their conserved charges.
The dipole ring was discovered essentially by educated guesswork, in very much the same way as the uncharged EmparanReall black ring. In 2006, Yazadjiev provided a different, algorithmic construction of a dipole ring solution. However, it cannot be employed to generate multiple rotations. In fact, until recently the techniques needed to carry out a systematic construction of multiply rotating dipole rings hadn't been fully understood.
In a 2011 paper with Maria J. Rodriguez and Amitabh Virmani we have remedied this situation for EinsteinMaxwelldilaton theory with a specific dilaton coupling constant. What enabled us to make progress is the fact that this theory is obtained by dimensionally reducing sixdimensional vacuum gravity on a circle. Therefore, by employing the inverse scattering method (ISM) of BelinskyZakharov on a carefully chosen seed in 6D we have been able to reproduce Emparan's dipole black ring.
The advantage of our construction is that this procedure can be generalized to generate a dipole ring with two independent angular momenta. What is more, conventional electric charge can also be added using this approach, i.e., the ISM in 6D, as shown in a paper with Maria J. Rodriguez and Oscar Varela. More recently a series of advances by ourselves and two other independent groups (Chen, Hong and Teo at Singapore; Feldman and Pomeransky at Novosibirsk) culminated in the discovery of the conjectured most general 5parameter family of asymptotically flat regular black rings in this theory.
High energy collisions in gravitational duals of confining gauge theories
The advent of socalled gauge/gravity dualities openned up a new window to study strongly coupled nonabelian gauge theories. Furthermore, these powerful tools can address farfromequilibrium problems. So it should come as no surprise that they have been widely used since the beginning of the millennium to study high energy collisions such as those conducted at the Relativistic Heavy Ion Collider (RHIC) or at the Large Hadron Collider (LHC).
The physics at play in these colliders is presumably described by Quantum Chromodynamics (QCD). However, the gravity dual of QCD is not presently known and usually the existing literature resorts to some kind of proxy for QCD, typically a largeN conformal gauge theory. These theories cannot display confinement behaviour  so characteristic of QCD at low energies. One might think that the effects of confinement are negligible for high energy collisions but the data collected at RHIC and LHC indicate otherwise: the temperature of the quarkgluon plasma formed by the collisions is not parametrically separated from the QCD confinement scale.
In a recent paper with Vitor Cardoso, Roberto Emparan, David Mateos and Paolo Pani we took a first step to include the effects of confinement in (holographically dual) high energy collisions, by considering an appropriate bulk geometry known as the AdSsoliton. The boundary dual theory exhibits confinement, behaving much like a waveguide and in particular featuring a mass gap.
In this work the collision process itself was modelled as simple as possible: the two incoming objects are assumed to be point particles, as well as the final static object (presumably a black hole for high enough energies), the collision is instantaneous and the gravitational radiation is treated in a linearized fashion. This is an adaptation of the Zero Frequency Limit framework, employed with great success in black hole collisions in asymptotically flat spacetimes. All internal details about the objects involved is lost in this approach. However, precisely this kind of information is expected to be irrelevant in ultrarelativistic collisions and our findings thus provide universal features of such processes.
