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

**Authors:** M. Cvetic, G. W. Gibbons, C. N. Pope  
**arXiv:** [1608.02202](https://arxiv.org/abs/1608.02202)  
**Date:** 2016-08-07  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1608.02202v1/

## Key points

- Study focuses on closed photon orbits in black holes from supergravity and other theories
- Photon spheres are regions where photons can orbit around a black hole, with stable and unstable orbits
- Only one photon sphere exists outside the event horizon in asymptotically flat solutions with regular event horizon and energy-momentum tensor satisfying strong energy condition
- Example of a Horndeski theory black hole accommodating both photon and anti-photon spheres due to violation of strong energy condition
- Study extends to asymptotically anti-de Sitter solutions in gauged supergravity, revealing projective symmetry akin to Schwarzschild-de Sitter metrics
- Accretion flows by perfect fluids within these metrics explored; alignment between Bondi's sonic horizon and photon sphere for radiation fluid but not for general polytropic equations of state
- Counterexamples presented challenging a conjecture proposed by Hod regarding these phenomena

## Summary

In their paper titled "Photon Spheres and Sonic Horizons in Black Holes from Supergravity and Other Theories," authors M. Cvetic, G. W. Gibbons, and C. N. Pope delve into the study of closed photon orbits within spherically-symmetric static solutions of supergravity theories, a Horndeski theory, and a theory of quintessence. They focus on the concept of photon spheres, which are regions where photons can orbit around a black hole, distinguishing between stable (anti-photon sphere) and unstable orbits. The researchers demonstrate that in all asymptotically flat solutions with a regular event horizon and energy-momentum tensor satisfying the strong energy condition, there exists only one photon sphere outside the event horizon. They provide an intriguing example of a Horndeski theory black hole whose metric accommodates both a photon sphere and an anti-photon sphere due to its violation of the strong energy condition. Furthermore, the study extends to asymptotically anti-de Sitter solutions in gauged supergravity, revealing the presence of projective symmetry akin to Schwarzschild-de Sitter metrics. This symmetry implies that unparameterized null geodesics remain consistent even when cosmological or gauge coupling constants approach zero. Additionally, the authors explore accretion flows by perfect fluids within these metrics. They find that for a radiation fluid, Bondi's sonic horizon aligns with the photon sphere; however, this alignment does not hold for general polytropic equations of state. Lastly, the paper presents counterexamples challenging a conjecture proposed by Hod in relation to these phenomena. With 44 pages and 3 figures, this comprehensive study sheds light on intricate dynamics surrounding photon spheres and sonic horizons in black holes across various theoretical frameworks.