Bound orbits and gravitational theory

Understand

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.