The Stability of an Isentropic Model for a Gaseous Relativistic Star

TL;DR

This paper demonstrates that a specific isentropic model for gaseous relativistic stars remains stable and gravitationally bound across a range of compactness ratios, challenging previous claims of instability.

Contribution

It proves the stability of the isentropic subclass of Buchdahl's solution for all compactness ratios up to 0.20, correcting earlier literature assertions.

Findings

Model is stable for all u in (0, 0.20]

Configuration remains gravitationally bound

Results align with theoretical expectations

Abstract

We show that the isentropic subclass of Buchdahl's exact solution for a gaseous relativistic star is stable and gravitationally bound for all values of the compactness ratio $u [\equiv (M/R)$, where $M$ is the total mass and $R$ is the radius of the configuration in geometrized units] in the range, $0 < u \leq 0.20$, corresponding to the {\em regular} behaviour of the solution. This result is in agreement with the expectation and opposite to the earlier claim found in the literature.