Entropy of matter on the Carroll geometry

Abstract

Two prescriptions, the expansion of near horizon of geometry and expansion of metric with zero limit of the expansion parameter $c$ (speed of light in vacuum), of constructing Carroll geometries are known to complement each other. The entropy of an ideal gas, confined in a box and kept very near 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 zero limit of the expansion parameter $c$. Therefore the present analysis re-assures the complementing nature of two ways of finding the Carroll geometry from the thermodynamical point of view.

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