Uniform density static fluid sphere in Einstein-Gauss-Bonnet gravity and its universality

TL;DR

This paper proves that the Schwarzschild interior solution for a uniform density static sphere remains universal across all spacetime dimensions in Einstein-Gauss-Bonnet gravity, extending Newtonian results to higher-order gravity theories.

Contribution

It establishes the necessary and sufficient condition for the universality of the Schwarzschild interior solution in Einstein-Gauss-Bonnet gravity, showing density constancy is key across all dimensions.

Findings

Universality of Schwarzschild interior solution holds in Einstein-Gauss-Bonnet gravity.

Constant density condition is necessary and sufficient for universality.

Result extends Newtonian gravity insights to higher-dimensional, nonlinear gravity theories.

Abstract

In Newtonian theory, gravity inside a constant density static sphere is independent of spacetime dimension. Interestingly this general result is also carried over to Einsteinian as well as higher order Einstein-Gauss-Bonnet (Lovelock) gravity notwithstanding their nonlinearity. We prove that the necessary and sufficient condition for universality of Schwarzschild interior solution describing a uniform density sphere for all $n\geq4$ is that its density is constant.