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.
Highlights
A decade ago, a new variable was introduced into black hole thermodynamics, as part of an extended thermodynamic framework [1]
It has the interpretation as the thermodynamic volume, V, dual to the pressure p ≡ −Λ=8π that is present if the cosmological constant Λ is dynamical
In general,4 this is somewhat mysterious from the black hole thermodynamics perspective—fixed pressure is more natural there since that is fixed Λ—but with a microscopic dual field theory identification such as the one presented here, progress can be made in examining the physics of the fixed volume sector. (This may be of use in furthering recent work [18,19,20] that has uncovered novel and potentially useful physics in the fixed volume sector of black hole thermodynamics.)
Summary
A decade ago, a new variable was introduced into black hole thermodynamics, as part of an extended thermodynamic framework [1]. In general, this is somewhat mysterious from the black hole thermodynamics perspective—fixed pressure is more natural there since that is fixed Λ—but with a microscopic dual field theory identification such as the one presented here, progress can be made in examining the physics of the fixed volume sector. While we do not prove the conjecture here, we find a microscopic phenomenon that seems to explain (or at least herald) the superentropicity on the gravity side, and it emerges precisely as a result of our microscopic identification of the thermodynamic volume V and as a consequence of working in the fixed V sector It works as follows: The standard (microscopic) CFT expression for the entropy, S, of the black holes which successfully. VI we discuss the results further, including ideas and prospects for extending this microscopic success to higher dimensions
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