Thermodynamics of black holes

Abstract

I n spite of the fundamental difficulties associated with the thermodynamics of self-gravitating systems, the objects known as black holes appear to conform to a very straightforward generalisation of standard laboratory thermodynamics. I n this review the generalised theory is examined in detail. It is shown how familiar concepts such as temperature, entropy, specific heats, phase transitions and irreversibility apply to systems containing black holes, and some concrete results of the theory are presented. The thermodynamic connection is based on Hawking's celebrated application of quantum theory to black holes, and in this review the quantum aspects are described in detail from several standpoints, both heuristic and otherwise. The precise mechanism by which the black hole produces thermal radiation, its nature and origin, and the energetics of back-reaction on the hole are reviewed. The thermal states of quantum holes are also treated using the theory of thermal Green functions, and the entropy of the hole is shown to be related to the loss of information about the quantum states hidden behind the event horizon. Some related topics such as accelerated mirrors and observers in Minkowski space, super-radiance from rotating holes and the thermodynamics of general self-gravitating systems are also briefly discussed.

Hawking radiation in different coordinate settings: complex paths approach

“…Only in exceptional cases in high symmetry will a set of detector exist that all register no particles, and this set may not even be free falling. These facts will have important implications in comparing the results of a freely falling detector in the Schwarzschild space-time [18] to that of the particle spectrum we obtain for the Lemaitre coordinates in Sec. (4.1).…”

“…The transformation in (18), which brings the interval to the form in (19) can, however, lead to a singular metric. The transformation in (18) can also lead to line elements of the form in (19), in which the metric component g 00 is negative and g 11 is positive.…”

Phase transition and thermodynamical geometry for Schwarzschild AdS black hole in AdS5 × S5 spacetime

“…For Kerr-Newmann black holes in Einstein-Maxwell theory, some heat capacities diverge at some black hole parameters. Based on this, Davies argued that some second order phase transitions will happen in Kerr-Newmann black holes [7][8][9]. For a Reissner-Nordström AdS (RN-AdS) black hole, such a phase transition was studied in some details in [10,11].…”

Thermodynamic geometry of charged rotating BTZ black holes

“…GTD incorporates Legendre invariance into the geometric structures of the phase space and equilibrium space so that the results do not depend on the choice of thermodynamic potential. The phase transition structure contained in the heat capacity of black holes [30] becomes completely integrated in the scalar curvature of the Legendre invariant metric so that a curvature singularity corresponds to a phase transition.…”