Thermodynamics of charged, rotating, and accelerating black holes
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Springer
Received: November 20, Revised: March 18, Accepted: April 9, Published: April 15,
2018 2019 2019 2019
Andr´ es Anabal´ on,a Finnian Gray,b,c Ruth Gregory,d,b David Kubizˇ n´ akb,c and Robert B. Mannc,b a
Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ib´ an ˜ez, Avenida Padre Hurtado 750, Vi˜ na del Mar 2520000, Chile b Perimeter Institute, 31 Caroline St., Waterloo, Ontario, N2L 2Y5, Canada c Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada, d Centre for Particle Theory, Durham University, South Road, Durham, DH1 3LE, U.K.
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: We show how to obtain a consistent thermodynamic description of accelerating asymptotically AdS black holes, extending our previous results by including charge and rotation. We find that the key ingredient of consistent thermodynamics is to ensure that the system is not over-constrained by including the possibility of varying the ‘string’ tensions that are responsible for the acceleration of the black hole, yielding a first law of full cohomogeneity. The first law assumes the standard form, with the entropy given by one quarter of the horizon area and other quantities identified by standard methods. In particular we compute the mass in two independent ways: through a Euclidean action calculation and by the method of conformal completion. The ambiguity in the choice of the normalization of the timelike Killing vector can be fixed by explicit coordinate transformation (in the case of rotation) to the standard AdS form or by holographic methods (in the case of charge). This resolves a long-standing problem of formulating the thermodynamics of accelerating black holes, opening the way to detailed studies of their phase behaviour. Keywords: Black Holes, AdS-CFT Correspondence ArXiv ePrint: 1811.04936
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP04(2019)096
JHEP04(2019)096
Thermodynamics of charged, rotating, and accelerating black holes
Contents 1
2 Generalized C-metric
2
3 Slowly accelerating black hole thermodynamics
4
4 On thermodynamics of the asymptotically flat C-metric
8
5 Discussion and summary
10
A Holographic stress tensor
11
1
Introduction
Black holes provide us with an invaluable and unique tool for probing the relationship between quantum physics and the gravitational force. From the early discoveries that black hole area and surface gravity respectively behave as thermodynamic entropy [1, 2] and temperature [3], a rich and varied range of thermodynamic behaviour of these objects has been uncovered [4], providing new insight into the underlying microscopic degrees of freedom that may be associated with quantum gravity. Amongst the panoply of black hole solutions, accelerating black holes have been somewhat less well understood. Described by the so-called C-metric [5–8], they have a conical singul
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