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 Phys. Rev. D 102, 106001 (2020) Upper bound on cross sections inside black holes and complexity growth rate 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 ABSTRACT This paper studies cross sections inside black holes and conjectures a universal inequality: in a static ( $d+1$)-dimensional asymptotically planar/spherical Schwarzschild-AdS spacetime of given energy  $E$ and AdS radius  ${\ell }_{\mathrm{AdS}}$, the “size of cross section” inside black holes is bounded by  $8\pi E{\ell }_{\mathrm{AdS}}/\left(d-1\right)$. To support this conjecture, it gives the proofs for cases with spherical/planar symmetries and some special cases without planar/spherical symmetries. As one corollary, it shows that the complexity growth rate in complexity-volume conjecture satisfies the upper bound argued by quantum information theory. This makes a first step toward proving the conjecture that the vacuum black hole has fastest complexity growth in the systems of same energy. It also finds a similar bound for asymptotically flat black holes, which gives us an estimation on the largest interior volume of a large evaporating black hole. 【关闭窗口】
 天津大学理学院 量子交叉研究中心   地址：天津津南区 雅观路135号 天津大学北洋园校区32楼146 Center for Joint Quantum Studies, School of Science, Tianjin University     Address : Yaguan Road 135, Jinnan District, 300350 Tianjin, P. R. China