  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.
