Universal bounds on the size of a black hole

Run-Qiu Yang; H. Lü

doi:10.1140/epjc/s10052-020-08521-7

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2020) 80: 949
https://doi.org/10.1140/epjc/s10052-020-08521-7

Regular Article – Theoretical Physics

Universal bounds on the size of a black hole

Run-Qiu Yang^a and H. Lü

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

^a aqiu@tju.edu.cn

Received: 14 July 2020
Accepted: 3 October 2020
Published online: 15 October 2020

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 $A_{ph, out}$ $A_{\mathrm {ph,out}}$ , the corresponding shadow area $A_{sh, out}$ $A_{\mathrm {sh,out}}$ and the horizon area $A_{H}$ $A_{{\mathcal {H}}}$ satisfy a series of universal inequalities $9 A_{H} / 4 \leq A_{ph, out} \leq A_{sh, out} / 3 \leq 36 π M^{2}$ $9A_{{\mathcal {H}}}/4\le A_{\mathrm {ph,out}}\le A_{\mathrm {sh,out}}/3\le 36\pi M^2$ , 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.

© The Author(s) 2020

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