Gravitational and Gravitoscalar Thermodynamics

TL;DR

This paper explores the thermodynamics of gravitational and gravitoscalar systems with specific boundary geometries, revealing new saddle points and conditions for stability and entropy bounds depending on the cosmological constant and scalar field parameters.

Contribution

It introduces the 'bag of gold' instanton as a new saddle point geometry for positive cosmological constant and analyzes stability and entropy bounds in gravitoscalar systems with varying parameters.

Findings

Existence of 'bag of gold' instantons only for positive cosmological constant.

Thermodynamical stability and entropy bounds are absent for Λ>0.

Stability and entropy bounds can be restored in gravitoscalar systems under certain conditions.

Abstract

Gravitational thermodynamics and gravitoscalar thermodynamics with $S^2 \times \mathbb{R}$ boundary geometry are investigated through the partition function, assuming that all Euclidean saddle point geometries contribute to the path integral and dominant ones are in the $B^3 \times S^1$ or $S^2 \times Disc$ topology sector. In the first part, I concentrate on the purely gravitational case with or without a cosmological constant and show there exists a new type of saddle point geometry, which I call the "bag of gold(BG) instanton," only for the $\Lambda>0$ case. Because of this existence, thermodynamical stability of the system and the entropy bound are absent for $\Lambda>0$, these being universal properties for $\Lambda \leq 0$. In the second part, I investigate the thermodynamical properties of a gravity-scalar system with a $\varphi^2$ potential. I show that when $\Lambda \leq 0$ and the boundary value of scalar field $J_{\varphi}$ is below some value, then the entropy bound and thermodynamical stability do exist. When either condition on the parameters does not hold, however, thermodynamical stability is (partially) broken. The properties of the system and the relation between BG instantons and the breakdown are discussed in detail.