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 \(9A_{{\mathcal {H}}}/4\le A_{\mathrm {ph,out}}\le A_{\mathrm {sh,out}}/3\le 36\pi M^2\), 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.

对于爱因斯坦引力中的静态黑洞，如果物质场满足一些一般条件，我们推测关于黑洞空间大小的三个特征参数，即最外层光子球面积\（A _ {\ mathrm {ph，out}} \ ），相应的阴影区域\（A _ {\ mathrm {sh，out}} \）和地平线区域\（A _ {{\ mathcal {H}}} \）满足一系列普遍不等式\（9A _ {{\ mathcal {H}}} / 4 \ le A _ {\ mathrm {ph，out}} \ le A _ {\ mathrm {sh，out}} / 3 \ le 36 \ pi M ^ 2 \），其中M是ADM质量。我们在球对称情况下提供了一个完整的证明，并在一般静态情况下提供了一些证据来支持它。我们还讨论了光子球在一般静态时空中的性质，并表明，与地平线类似，光子球也是时空的共形不变结构。