标题： 束缚轨道和引力理论 显示英文标题

标题： Bound orbits and gravitational theory

摘要： 可以很容易地证明，围绕静态源的束缚轨道只能存在于4维空间，而在其他任何维度都不可能存在任何长程力。 这不仅适用于麦克斯韦的电磁理论和牛顿的引力，也适用于爱因斯坦的引力理论。 与麦克斯韦电动力学和牛顿引力不同，广义相对论在洛埃洛克引力中有一个自然的高维推广，该理论显著地允许在所有偶数维d=2N+2中存在围绕静态黑洞的束缚轨道，其中$N$是洛埃洛克多项式作用量的次数。 这一结果与经典力学中的伯特兰定理一样普遍，在伯特兰定理中，闭合轨道的存在唯一地指出了长程中心力的平方反比定律。 显示英文摘要

摘要： 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.