Comments on Entropy Calculations in Gravitational Systems

TL;DR

This paper reviews and critiques various methods for calculating entropy in gravitational systems, proposing an alternative Hamiltonian approach that resolves some issues in higher-order calculations and addressing sign ambiguities in de Sitter thermodynamics.

Contribution

It introduces a Hamiltonian method for gravitational entropy calculations that overcomes limitations of Euclidean approaches at higher orders.

Findings

Hamiltonian approach justifies Euclidean calculations at lowest order

Addresses sign ambiguities in de Sitter thermodynamics

Provides insights into entropy calculations for various gravitational backgrounds

Abstract

We discuss the logic of, and some puzzles in, the various approaches to thermodynamics of gravitational systems. In particular the blackhole, deSitter (dS), black hole in dS (SdS) and in Anti-deSitter SAdS backgrounds are considered. After reviewing the original calculations of Hawking and Gibbons we discuss an alternative Hamiltonian method. This justifies the lowest order Euclidean calculation but is free of the problems associated with the latter when going to higher orders. To conclude we address the sign issue in dS thermodynamics.