Upper bound about cross-sections inside black holes and complexity growth rate
arXiv:1911.12561 · doi:10.1103/PhysRevD.102.106001
Abstract
This paper studies cross-sections inside black holes and conjectures a universal inequality: in a static -dimensional asymptotically planar/spherical Schwarzschild-AdS spacetime of given energy and AdS radius , the ``size of cross-section'' inside black holes is bounded by . 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.
improve the proof; more examples are added
References in corpus (12)
- The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
- Complexity and Shock Wave Geometries
- The Page curve of Hawking radiation from semiclassical geometry
- On the Time Dependence of Holographic Complexity
- How big is a black hole?
- Present status of the Penrose inequality
- Information Flow in Black Hole Evaporation
- On the time dependence of holographic complexity in a dynamical Einstein-dilaton model
- Holographic complexity of anisotropic black branes
- Entanglement Entropy and Subregion Complexity in Thermal Perturbations around Pure-AdS Spacetime
- Quantum Penrose Inequality
- Quantum Information Bound on the Energy