Quantum mechanics

Gauss–Bonnet gravity

SPHERES

Spacetime

Mathematical physics

Einstein

Classical mechanics

Universality (dynamical systems)

Cosmological constant

Physics

Astronomy

Newtonian fluid

Schwarzschild metric

General relativity

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology

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 the Schwarzschild interior solution describing a uniform density sphere for all $n\ensuremath{\ge}4$ is that its density is constant.

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