The fate of observers in circular motion

TL;DR

This paper explores how energy loss affects the stability and fate of particles in circular orbits across different gravity theories, revealing universal behaviors and proposing a new metric with unique orbital properties.

Contribution

It demonstrates the universal impact of energy dissipation on orbit stability in any gravity theory respecting the weak equivalence principle and introduces a toy metric with an unbound innermost stable orbit.

Findings

Energy loss causes particles to plunge or settle at potential minima.

The relation between particle energy and orbit stability is universal.

A new metric with an unbound innermost stable orbit is constructed.

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.