# Negative specific heat of black-holes from Fluid-Gravity Correspondence

## TL;DR

This paper uses fluid-gravity correspondence and linear response theory to explain why Schwarzschild black holes have negative specific heat, and discusses conditions under which other black holes can have positive specific heat.

## Contribution

It provides a novel statistical mechanical explanation for black hole specific heat behavior using horizon-fluid fluctuations and extends the canonical ensemble approach to asymptotically flat black holes.

## Key findings

- Schwarzschild black holes exhibit negative specific heat due to horizon-fluid fluctuations.
- Kerr-Newman and AdS black holes can have positive specific heat.
- The approach advances the understanding of black hole thermodynamics in flat space-times.

## Abstract

Black-holes in asymptotically flat space-times have negative specific heat --- they get hotter as they loose energy. A clear statistical mechanical understanding of this has remained a challenge. In this work, we address this issue using fluid-gravity correspondence which aims to associate fluid degrees of freedom to the horizon. Using linear response theory and the teleological nature of event horizon, we show explicitly that the fluctuations of the horizon-fluid lead to negative specific heat for Schwarzschild black Hole. We also point out how the specific heat can be positive for Kerr-Newman or AdS black holes. Our approach constitutes an important advance as it allows us to apply canonical ensemble approach to study thermodynamics of asymptotically flat black-hole space-times.