A Microscopic Description of Thermodynamic Volume in Extended Black Hole Thermodynamics

TL;DR

This paper explores the thermodynamic volume of black holes within the AdS/CFT framework, revealing how super-entropicity arises from CFT entropy over-counting and linking specific heat to black hole stability.

Contribution

It provides the first field theory analysis of black hole thermodynamic volume, connecting super-entropicity to CFT entropy over-counting and explaining thermodynamic stability.

Findings

Thermodynamic volume can cause black holes to be super-entropic.

Super-entropicity results from CFT entropy over-counting via the Cardy formula.

Specific heat at constant volume indicates black hole stability or instability.

Abstract

Using the fact that theories of gravity with asymptotically three-dimensional anti-de Sitter geometries have dual descriptions as two-dimensional conformal field theories (CFTs), we present the first study in field theory of the thermodynamic volume of various black hole solutions. We explain in general two-dimensional CFT terms why the presence of a thermodynamic volume can render certain black hole solutions "super-entropic". Super-entropicity simply results from the fact that the Cardy formula, which gives the gravitational Bekenstein-Hawking entropy, can over-count the CFT entropy. The examples of charged Banados, Teitelbiom and Zanelli (BTZ) black holes and generalized exotic BTZ black holes are described. These observations help explain why the specific heat at constant volume can signal the instability of such solutions, as recently conjectured.