https://doi.org/10.1140/epjc/s10052-024-12753-2
Regular Article - Theoretical Physics
Bulk-boundary thermodynamics of charged black holes in higher-derivative theory
Indian Institute of Science Education and Research Bhopal, Bhopal Bypass Road, Bhauri, 420066, Bhopal, India
Received:
23
December
2023
Accepted:
28
March
2024
Published online:
6
May
2024
The connection between bulk and boundary thermodynamics in Einstein–Maxwell theory is well established using AdS/CFT correspondence. In the context of general higher-derivative gravity coupled to a U(1) gauge field, we examine the resemblance of the first law of thermodynamics between bulk and boundary, followed by an extended phase space description on both sides. Higher-derivative terms related to different powers of the string theory parameter 
emerged from a consistent truncation in the bulk supergravity action. We demonstrate that one must include the fluctuation of in the bulk thermodynamics as a bookkeeping tool to match the bulk first law and Smarr relation with the boundary side. Consequently, the Euler relation and the boundary first law are altered by adding two central charges 
To support our general conclusion, we consider the black hole in Gauss–Bonnet gravity and the general four-derivative theory. Finally, we examine the bulk and boundary aspects of the extended phase space description for higher-derivative-corrected black holes.
© The Author(s) 2024
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