Boundary Counterterms and the Thermodynamics of 2-D Black Holes

TL;DR

This paper develops a Hamilton-Jacobi based method to analyze the thermodynamics of 2D type 0A black holes, deriving universal expressions for entropy and mass, and verifying thermodynamic laws.

Contribution

It introduces a novel boundary counterterm approach for 2D black hole thermodynamics, providing universal formulas and testing their consistency with thermodynamic principles.

Findings

Recovered standard results for Witten's black hole

Derived universal expressions for entropy and mass

Verified the first law of thermodynamics for 2D black holes

Abstract

We utilize a novel method to study the thermodynamics of two dimensional type 0A black holes with constant RR flux. Our approach is based on the Hamilton-Jacobi method of deriving boundary counterterms. We demonstrate this approach by recovering the standard results for a well understood example, Witten's black hole. Between this example and the 0A black hole we find universal expressions for the entropy and black hole mass, as well as the infra-red divergence of the partition function. As a non-trivial check of our results we verify the first law of thermodynamics for these systems. Our results for the mass disagree with the predictions of a proposed matrix model dual of the 0A black hole.