Photon Spheres and Sonic Horizons in Black Holes from Supergravity and Other Theories

TL;DR

This paper investigates photon spheres and sonic horizons in various black hole solutions from supergravity, Horndeski, and quintessence theories, revealing uniqueness properties, exceptions, and connections to fluid accretion phenomena.

Contribution

It demonstrates the uniqueness of photon spheres outside black holes with regular horizons under certain energy conditions and explores their relation to sonic horizons in fluid accretion.

Findings

One photon sphere outside black holes with regular horizons under strong energy condition.

Existence of black hole solutions with both photon and anti-photon spheres in Horndeski theory.

Bondi's sonic horizon coincides with the photon sphere for radiation fluids.

Abstract

We study closed photon orbits in spherically-symmetric static solutions of supergravity theories, a Horndeski theory, and a theory of quintessence. These orbits lie in what we shall call a photon sphere (anti-photon sphere) if the orbit is unstable (stable). We show that in all the asymptotically flat solutions we examine that admit a regular event horizon, and whose energy-momentum tensor satisfies the strong energy condition, there is one and only one photon sphere outside the event horizon. We give an example of a Horndeski theory black hole (whose energy-momentum tensor violates the strong energy condition) whose metric admits both a photon sphere and an anti-photon sphere. The uniqueness and non-existence also holds for asymptotically anti-de Sitter solutions in gauged supergravity. The latter also exhibit the projective symmetry that was first discovered for the Schwarzschild-de Sitter metrics: the unparameterised null geodesics are the same as when the cosmological or gauge coupling constant vanishes. We also study the closely related problem of accretion flows by perfect fluids in these metrics. For a radiation fluid, Bondi's sonic horizon coincides with the photon sphere. For a general polytropic equation of state this is not the case. Finally we exhibit counterexamples to a conjecture of Hod's.