Static spherically symmetric star in Gauss-Bonnet gravity

TL;DR

This paper investigates static spherically symmetric stars within Gauss-Bonnet gravity, revealing how the Gauss-Bonnet term alters energy bounds and redshift limits, and demonstrating the applicability of stability theorems.

Contribution

It provides an exact internal solution for stars in Gauss-Bonnet gravity and shows how the Gauss-Bonnet term affects stellar properties and stability criteria.

Findings

Gauss-Bonnet term changes thermal and gravitational energies.

Upper redshift bound depends on stellar density in this theory.

Stability theorems from general relativity hold in Gauss-Bonnet gravity.

Abstract

We explore static spherically symmetric stars in the Gauss-Bonnet gravity without cosmological constant, and present an exact internal solution which attaches to the exterior vacuum solution outside stars. It turns out that the presence of the Gauss-Bonnet term with a positive coupling constant completely changes thermal and gravitational energies, and the upper bound of red shift of spectral lines from the surface of stars. Unlike in general relativity, the upper bound of red shift is dependent on the density of stars in our case. Moreover, we have proven that two theorems for judging the stability of equilibrium of stars in general relativity can be hold in Gauss-Bonnet gravity.