Eur. Phys. J. C  80:949 (2020)

Universal bounds on the size of a black hole

Run-Qiu Yang^*, H. Lü

Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Yaguan Road 135, Jinnan District, Tianjin 300350, People’s Republic of China

Abstract

For static black holes in Einstein gravity, if matter fields satisfy a few general conditions, we conjecture that three characteristic parameters about the spatial size of black holes, namely the outermost photon sphere area A_ph,out, the corresponding shadow area A_sh,out and the horizon area A_H satisfy a series of universal inequalities 9A_H/4≤A_ph,out≤A_sh,out/3≤36πM², where M is the ADM mass. We present a complete proof in the spherically symmetric case and some pieces of evidence to support it in general static cases. We also discuss the properties of the photon spheres in general static spacetimes and show that, similar to horizon, photon spheres are also conformal invariant structures of the spacetimes.