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arXiv · 1911.12561

Upper bound about cross-sections inside black holes and complexity growth rate

Run-Qiu Yang
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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 $\ell_{\text{AdS}}$, the ``size of cross-section'' inside black holes is bounded by $8\pi E\ell_{\text{AdS}}/(d-1)$. 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 towards 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.

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Run-Qiu Yang. 2019-11-28. Upper bound about cross-sections inside black holes and complexity growth rate. https://doi.org/10.1103/physrevd.102.106001

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