Thermodynamic Volume of Cosmological Solitons

TL;DR

This paper derives explicit formulas for the thermodynamic volume of Eguchi-Hanson solitons in odd dimensions, analyzing inequalities and mass conjectures to deepen understanding of their thermodynamic properties.

Contribution

It provides the first explicit expressions for the thermodynamic volume inside and outside cosmological horizons of Eguchi-Hanson solitons in general odd dimensions, including analysis of inequalities and mass conjectures.

Findings

Thermodynamic volume formulas are well-defined regardless of regularity conditions.

The reverse isoperimetric inequality is generally not satisfied, except in a narrow parameter range.

The outer mass satisfies the maximal mass conjecture and the volume remains positive.

Abstract

We present explicit expressions of the thermodynamic volume inside and outside the cosmological horizon of Eguchi-Hanson solitons in general odd dimensions. These quantities are calculable and well-defined regardless of whether or not the regularity condition for the soliton is imposed. For the inner case, we show that the reverse isoperimetric inequality is not satisfied for general values of the soliton parameter $a$, though a narrow range exists for which the inequality does hold. For the outer case, we find that the mass $M_{out}$ satisfies the maximal mass conjecture and the volume is positive. We also show that, by requiring $M_{out}$ to yield the mass of dS spacetime when the soliton parameter vanishes, the associated cosmological volume is always positive.