Universal bounds on the size of a black hole

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

arXiv commentMatch the published version

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• A generalization of photon sphere based on escape/capture cone
• Uniqueness of photon sphere for Reissner-Nordström electric-magnetic system
• New look at AdS black holes with conformal scalar hair
• Gravitational Collapse: Generalizing Oppenheimer-Snyder and a Conjecture on Horizon Formation Time
• Higher-dimensional electric-magnetic photon sphere uniqueness
• Uniqueness of electric-magnetic spacetimes with massive particle
• Bounds on the photon sphere radius for spherically symmetric black holes in n-dimensional Einstein gravity