Bound orbits and gravitational theory

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.

7 pages, 1 pdf figure

References in corpus (3)

• Generalized Vaidya Spacetime in Lovelock Gravity and Thermodynamics on Apparent Horizon
• Black Holes in Pure Lovelock Gravities
• Komar Integrals in Higher (and Lower) Derivative Gravity

Cited by in corpus (27)

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• Buchdahl compactness limit for a pure Lovelock static fluid star
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• Universality of isothermal fluid spheres in Lovelock gravity
• Compact objects in pure Lovelock theory
• On Lovelock analogues of the Riemann tensor
• Stability and existence analysis of static black holes in pure Lovelock theories
• Pure Lovelock black hole in the dimension, $d=3N+1$, is stable
• 1/r potential in higher dimensions
• Buchdahl-Vaidya-Tikekar model for stellar interior in pure Lovelock gravity - II
• Pure Lovelock Kasner metrics
• Maximum Force in Modified Gravity Theories
• Pure Lovelock Gravity regular black holes
• Maximum Force for Black Holes and Buchdahl Stars
• Effect of dynamical noncommutativity on the limiting mass of white dwarfs
• Generalized Gödel universes in higher dimensions and pure Lovelock gravity
• Understanding General Relativity after 100 years: A matter of perspective
• Pure Gauss-Bonnet NUT Black Hole Solution: I
• Rotating black hole in Einstein and pure Lovelock gravity
• Connecting quasi-normal modes with causality in Lovelock theories of gravity
• Study of motion around a static black hole in Einstein and Lovelock gravity
• Conserved quantities for black hole solutions in pure Lovelock gravity
• Stable bound orbits around static Einstein-Gauss-Bonnet black holes
• On the Photon Motion Near a Five-Dimensional Schwarzschild Black Hole
• Pure Gauss-Bonnet NUT Black Hole Solution: II
• Extrinsic black hole uniqueness in pure Lovelock gravity
• Lower bound of black hole hair in pure Lovelock theory of gravity