The fate of observers in circular motion

Abstract

In Newtonian physics or in general relativity, energy dissipation causes observers moving along circular orbits to slowly spiral towards the source of the gravitational field. We show that the loss of energy has the same effect in any theory of gravity respecting the weak equivalence principle, by exhibiting an intimate relation between the energy of a massive test particle and the stability of its orbit. Ultimately, massive particles either plunge, or are driven towards minima of the generalized Newtonian potential, where they become static. In addition, we construct a toy metric which displays an unbound innermost stable circular orbit, allowing particles that reach this orbit to be expelled away.

6 pages, 1 figure; accepted for publication in PRD

References in corpus (5)

• The Confrontation between General Relativity and Experiment
• Light ring stability in ultra-compact objects
• Light rings as observational evidence for event horizons: long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects
• Ring Formation around Giant Planets by Tidal Disruption of a Single Passing Large Kuiper Belt Object
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Cited by in corpus (7)

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• Static spheres around spherically symmetric black hole spacetime
• Aschenbach effect and circular orbits in static and spherically symmetric black hole backgrounds
• Static spheres and Aschenbach effect for black holes in massive gravity
• Topological charge and black hole photon spheres in massive gravity
• There and back again: Outspiraling motion in non-Kerr compact objects