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Black hole-de Sitter space as the fastest transmitter and receiver

Rong-Gen Cai, Li Hu, Shao-Jiang Wang

Abstract

It is well-known that the unitary nature of black hole evaporation enforces its entropy evolution to follow the Page curve. In this Letter, we find that the quantum speed limit on how fast a quantum system can evolve unitarily, when the maximal information transmission bound is saturated, will slow down the would-be divergent decreasing rate of dynamical black-hole entropy at the very end of the Hawking evaporation, during which the Penrose inequality from cosmic censorship conjecture is exactly saturated. Therefore, an evaporating Schwarzschild black hole is the fastest transmitter of information in nature. Further applying the maximal information transmission bound to an effective-field-theory description of a de Sitter space would roughly reproduce the trans-Planckian censorship conjecture, indicating the de Sitter space as the fastest receiver of information in nature.

Black hole-de Sitter space as the fastest transmitter and receiver

Abstract

It is well-known that the unitary nature of black hole evaporation enforces its entropy evolution to follow the Page curve. In this Letter, we find that the quantum speed limit on how fast a quantum system can evolve unitarily, when the maximal information transmission bound is saturated, will slow down the would-be divergent decreasing rate of dynamical black-hole entropy at the very end of the Hawking evaporation, during which the Penrose inequality from cosmic censorship conjecture is exactly saturated. Therefore, an evaporating Schwarzschild black hole is the fastest transmitter of information in nature. Further applying the maximal information transmission bound to an effective-field-theory description of a de Sitter space would roughly reproduce the trans-Planckian censorship conjecture, indicating the de Sitter space as the fastest receiver of information in nature.

Paper Structure

This paper contains 28 equations, 1 figure.

Figures (1)

  • Figure 1: The time-derivative of black-hole entropy (green) saturates the Pendry' bound limited by the quantum-speed limit (QSL), equivalent to the cosmic censorship conjecture (CCC), consisting of both the instantaneous (blue) and average (red) versions of the Bremermann-Bekenstein bounds at early/late or very late stages with dense or sparse energy spectrum, respectively.