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Black holes and hot shells in the Euclidean path integral approach to quantum gravity

Oct. 06 - 14:30 - 2022

Speaker: José Sande Lemos (CENTRA, Physics Department, IST)

Title: Black holes and hot shells in the Euclidean path integral approach to quantum gravity


Microscopic gravitational systems involving black holes and matter present quantum and thermodynamic properties that are worth of study. Due to the breaking of the vacuum from the strong gravitational field near the event horizon of a black hole, particles, such as gravitons or other matter fields, are emitted to infinity with a definite temperature, the Hawking temperature. Left by itself, a black hole loses mass in this emission process until it eventually disappears. To understand more deeply the connection and conversion between black holes and hot matter fields, one has thus to enclose the black hole and the hot matter inside a heat reservoir which is maintained at constant temperature and constant radius, and which in turn characterizes the canonical ensemble of statistical mechanics. A thermodynamic treatment for the system black hole plus hot matter is then possible. We model the hot matter fields by a hot thin shell that surrounds a black hole and is inside the heat reservoir. To work out the quantum partition function, from which the thermodynamics of the system emerges, we use the Euclidean path integral approach to quantum gravity that identifies the path integral of the gravitational system with the partition function itself. In a zeroth order, semiclassical, evaluation of the path integral, one computes the Euclidean classical action of the system which, at this order, is equal to the system's thermodynamic free energy divided by the temperature. Several important consequences related to the energy, the temperature stratification, the entropy, and the thermodynamic stability of the system unfold in a natural way. A most significant result is the finding of the various possible thermodynamic phases of the ensemble, specifically, pure black hole spaces, pure hot shell spaces, hot shell with a black hole spaces, and hot flat spaces, and the establishing of the possible phase transitions between them through the identification of the ground state phase of the ensemble once a temperature equation of state for the matter in the hot shell is given. Yet another result, connected with the conversion of pure black holes into curved spaces with hot matter in the form of hot thin shells and vice versa, is that the systems in some instances perform as black hole thermodynamic mimickers and in another instances act as authentic dynamic and geometric mimickers. The precise setting and all these results will be explained in some detail along the seminar.

Room: Sala de Reuniões e Seminários (2-8.3) (2nd Floor of Physics Building)

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