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