Bounds on 2m/r for static perfect fluids

TL;DR

This paper derives sharper bounds on the mass-to-radius ratio for static perfect fluid spheres in relativity by imposing bounds on the pressure-to-density ratio, refining the classical Buchdahl limit.

Contribution

It introduces a new inequality that depends on the bound of p/ρ, providing tighter constraints than Buchdahl's original limit under certain energy conditions.

Findings

For p/ρ ≤ 1, the bound is 2M/R ≤ 6/7.

The inequality depends explicitly on the imposed p/ρ bound.

Provides a generalized framework for bounds based on energy conditions.

Abstract

For spherically symmetric relativistic perfect fluid models, the well-known Buchdahl inequality provides the bound $2 M/R \leq 8/9$, where $R$ denotes the surface radius and $M$ the total mass of a solution. By assuming that the ratio $p/\rho$ be bounded, where $p$ is the pressure, $\rho$ the density of solutions, we prove a sharper inequality of the same type, which depends on the actual bound imposed on $p/\rho$. As a special case, when we assume the dominant energy condition $p/\rho \leq 1$, we obtain $2 M/R \leq 6/7$.