Exact barotropic distributions in Einstein-Gauss-Bonnet gravity

TL;DR

This paper derives new exact solutions for spherically symmetric perfect fluid distributions in 5-dimensional Einstein-Gauss-Bonnet gravity, demonstrating physically viable models with barotropic equations of state.

Contribution

It introduces a method to obtain exact solutions in Einstein-Gauss-Bonnet gravity using Frobenius series, including polynomial models and the 5D Einstein limit.

Findings

Solutions satisfy energy conditions

Models admit barotropic and isothermal equations of state

Interior solutions are physically well-behaved

Abstract

New exact solutions to the field equations in the Einstein--Gauss--Bonnet modified theory of gravity for a 5--dimensional spherically symmetric static distribution of a perfect fluid is obtained. The Frobenius method is used to obtain this solution in terms of an infinite series. Exact solutions are generated in terms of polynomials from the infinite series. The 5--dimensional Einstein solution is also found by setting the coupling constant to be zero. All models admit a barotropic equation of state. Linear equations of state are admitted in particular models with the energy density profile of isothermal distributions. We examine the physicality of the solution by studying graphically the isotropic pressure and the energy density. The model is well behaved in the interior and the weak, strong and dominant energy conditions are satisfied.