The Impact of $f(\mathcal{G}, T)$ Gravity on the Evolution of Cavity in the Cluster of Stars

TL;DR

This study explores how modified Gauss-Bonnet gravity influences the evolution of cavities within star clusters, revealing dark matter's significant role in this process through analytical models and specific stellar case analysis.

Contribution

It provides analytical solutions in $f( ext{G}, T)$ gravity for cavity evolution in star clusters, highlighting dark matter's impact, which is a novel aspect of this research.

Findings

Dark matter significantly affects cavity evolution.

Analytical solutions in $f( ext{G}, T)$ gravity are derived.

Cavities at boundaries satisfy Darmois conditions.

Abstract

This paper analyzes the evolution of cavities for the cluster of stars in the context of modified Gauss-Bonnet gravity. For this purpose, we assume a spherically symmetric geometry with locally anisotropic fluid distribution. It is assumed that the proper radial distance among neighboring stellar components stays unchanged during purely areal evolution stage. We provide some analytical solutions by using general formulism in $f(\mathcal{G}, T)$ gravitation theory. The thick-shells cavities at one or both boundary surfaces are found to satisfy the Darmois conditions. Moreover, we also investigate the physical behavior of cavity models by considering the stellar $4U 1820-30$. We conclude that the dark matter has a strong impact on the evolution of cavities in the cluster of stars.