Abstract
We discuss the thermodynamics of an array of collinear black holes which may be accelerating. We prove a general First Law, including variations in the tensions of strings linking and accelerating the black holes. We analyse the implications of the First Law in a number of instructive cases, including that of the C-metric, and relate our findings to the previously obtained thermodynamics of slowly accelerating black holes in anti-de Sitter spacetime. The concept of thermodynamic length is found to be robust and a Christoudoulou-Ruffini formula for the C-metric is shown.
Highlights
Reviewed by: Adil Belhaj, Mohammed V University, Morocco Vladimir Manko, Instituto Politécnico Nacional de México (CINVESTAV), Mexico Andrei Zelnikov, University of Alberta, Canada
It is interesting to explore some sample accelerating and non-accelerating black hole arrays to gain an understanding of the interdependency of black hole entropy, and to see how the strings contribute to the thermodynamic system as well as cross-checking against known results
To sum up: we have proven a thermodynamic First Law for a composite system of black holes, both accelerating and isolated
Summary
Black hole thermodynamics is a rich subject, straddling both the classical and quantum aspects of gravity. The first law of thermodynamics in gravitational systems has been more comprehensively understood as an extended thermodynamical law by including pressure in the guise of variations in vacuum energy [6,7,8,9,10], and a more complete understanding of the nature of “M” for the black hole has emerged as the enthalpy of the system [7] (see [11] for a review) These attempts at understanding the First Law have largely considered single, isolated, black holes, as in the Kerr-Newman family of solutions. One should expect that if gravitational solutions are truly representatives of a first law of thermodynamics in the classical limit, one will find common features no matter the number of black holes involved We demonstrate this here, by calculating variations of an array of collinear black holes—connected by strings—which may be accelerated by external strings so as to form an acceleration horizon.
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