Anisotropic generalization of Buchdahl bound for specific stellar models

TL;DR

This paper extends the Buchdahl bound for compact stars by incorporating anisotropic effects, revealing how pressure anisotropy influences the maximum possible compactness of stellar models.

Contribution

It provides a generalized anisotropic Buchdahl limit for specific stellar solutions, connecting anisotropy with maximum compactness and geometry.

Findings

Anisotropy affects the maximum allowed compactness of stars.

The classical Buchdahl limit is recovered in the isotropic case.

Pressure anisotropy influences the star's stability and structure.

Abstract

Anisotropy is one factor that appears to be significantly important in the studies of relativistic compact stars. In this paper, we make a generalization of the Buchdahl limit by incorporating an anisotropic effect for a selected class of exact solutions describing anisotropic stellar objects. In the isotropic case of a homogeneous distribution, we regain the Buchdahl limit $2M/R \leq 8/9$. Our investigation shows a direct link between the maximum allowed compactness and pressure anisotropy vi-a-vis geometry of the associated $3$-space.