Abstract
It can be easily shown that bound orbits around a static source can only exist in four dimensions for any force driven by the Laplace equation. This is true not only for Maxwell's electromagnetism and Newton's gravity, but for Einstein's theory of gravitation as well. In contrast to Maxwell's electrodynamics and Newton's gravity, general relativity has a natural and remarkable generalization in higher dimensions in Lovelock gravity. However, it is not Laplace driven and hence admits bound orbits around a static black hole in all even $D=2N+2$ dimensions, where $N$ is the degree of the Lovelock polynomial action. This is as general a result as Bertrand's theorem of classical mechanics, in which the existence of closed orbits uniquely singles out the inverse square law for a long-range central force.
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