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