Buchdahl's inequality in five dimensional Gauss-Bonnet gravity

TL;DR

This paper extends the Buchdahl limit to five-dimensional Gauss-Bonnet gravity, showing how the bound depends on the coupling constant and allowing stable stars with extra mass near the horizon.

Contribution

It generalizes the Buchdahl inequality to five-dimensional Gauss-Bonnet gravity, revealing the dependence on the coupling constant and stellar structure, which differs from general relativity.

Findings

For positive coupling, the bound depends on stellar structure and central energy density.

Stable stars can exist arbitrarily close to the event horizon with extra mass.

For negative coupling, the bound is more restrictive than in general relativity.

Abstract

The Buchdahl limit for static spherically symmetric isotropic stars is generalised to the case of five dimensional Gauss-Bonnet gravity. Our result depends on the sign of the Gauss-Bonnet coupling constant $\alpha$. When $\alpha>0$, we find, unlike in general relativity, that the bound is dependent on the stellar structure, in particular the central energy density. We find that stable stellar structures can exist arbitrarily close to the event horizon. Thus stable stars can exist with extra mass in this theory compared to five dimensional general relativity. For $\alpha<0$ it is found that the Buchdahl bound is more restrictive than the general relativistic case.