Bound on photon circular orbits in general relativity and beyond

TL;DR

This paper derives bounds on the location of photon circular orbits in various gravity theories, revealing that these bounds can be either upper or lower depending on matter content, impacting observable signatures of compact objects.

Contribution

It introduces new bounds on photon circular orbits in general relativity and beyond, including higher dimensions and alternative gravity theories, with implications for astrophysical observations.

Findings

Bounds can be lower or upper depending on matter content.

Modified bounds in higher-dimensional and Lovelock gravity.

Implications for quasi-normal modes and shadow radius.

Abstract

Existence of a photon circular orbit can tell us a lot about the nature of the underlying spacetime, since it plays a pivotal role in the understanding of the characteristic signatures of compact objects, namely the quasi-normal modes and shadow radius. For this purpose, determination of the location of the photon circular orbit is of utmost importance. In this work, we derive bounds on the location of the photon circular orbit around compact objects within the purview of general relativity and beyond. As we have explicitly demonstrated, contrary to the earlier results in the context of general relativity, the bound on the location of the photon circular orbit is not necessarily an upper bound, rather depending on the matter content it is possible to arrive at a lower bound as well. This have interesting implications for the quasi-normal modes and shadow radius, the two key observables related to the strong field tests of gravity. Besides discussing the bound for higher dimensional general relativity, we have also considered how the bound on the photon circular orbits gets modified in the braneworld scenario, for pure Lovelock and general Lovelock theories of gravity. Implications of these results for compact objects have also been discussed.