Entropy of matter on the Carroll geometry

TL;DR

This paper explores how Carroll geometries, constructed via two different methods, relate to the entropy of matter near horizons, demonstrating their complementary nature through thermodynamical analysis.

Contribution

It shows that two known prescriptions for Carroll geometries are complementary by linking them to the entropy of matter near horizons.

Findings

Entropy depends on the transverse area of the container.

Carroll geometry constructed via metric expansion relates to thermodynamics.

The two prescriptions for Carroll geometry are shown to be complementary.

Abstract

Two prescriptions for the construction of Carroll geometries, the expansion of geometric variables near horizon and the expansion of metric with zero limit of the expansion parameter $c$ (speed of light in vacuum), are known to complement each other. The entropy of an ideal gas, confined in a box and kept very close to the horizon, depends on the transverse area of the container. We show this by using the Carroll geometry constructed through the expansion of the metric and then taking the zero limit of the expansion parameter $c$. Therefore, the present analysis assures the complementing nature of two ways of finding the Carroll geometry from the thermodynamical point of view.