Bound orbits and gravitational theory

TL;DR

This paper demonstrates that bound orbits around static sources are limited to four dimensions in classical theories but can exist in higher even dimensions within Lovelock gravity, extending classical results to higher-dimensional spacetime.

Contribution

It shows that Lovelock gravity admits bound orbits in all even dimensions, generalizing classical orbit restrictions and extending the understanding of gravitational behavior in higher dimensions.

Findings

Bound orbits exist only in 4D for classical theories.

Lovelock gravity allows bound orbits in all even dimensions.

Classical orbit restrictions are extended to higher-dimensional gravity theories.

Abstract

It can be easily shown that bound orbits around a static source can exist only in 4 dimension and in none else for any long range force. This is so not only for Maxwell's electromagnetic and Newton's gravity but also for Einstein's gravitation theory. In contrast to Maxwell's electrodynamics and Newton's gravity, GR has a natural higher dimensional generalization in Lovelock gravity which remarkably admits bound orbits around a static black hole in all even d=2N+2 dimensions where $N$ is degree of Lovelock polynomial action. This is as general a result as Bertrand's theorem of classical mechanics in which existence of closed orbits uniquely singles out the inverse square law for a long range central force.