The unstable null circular geodesic features the spherically symmetrical asymptotically flat black hole

TL;DR

This paper investigates the unstable null circular geodesic around spherically symmetric, asymptotically flat black holes, revealing its properties and implications for massless particle orbits.

Contribution

It provides an analytical demonstration of the instability of null circular geodesics in such spacetimes, applicable to all asymptotically flat, spherically symmetric black holes.

Findings

Null circular geodesics are unstable.

Orbital period is the shortest among all paths.

Results are general for asymptotically flat, spherically symmetric spacetimes.

Abstract

We analyse the massless particles orbiting a spherically symmetric, asymptotically flat black hole with a radius equal to the photon sphere and a circular geodesic. Asymptotic observers record the orbital period of the null circular geodesic as the lowest among all possible paths around the compact object. We proceed with the analytical study of massless particle motion to demonstrate the instability of an orbit with null circularity. Furthermore, our results apply to any asymptotically flat and spherically symmetric spacetime.