Black hole complementarity with the generalized uncertainty principle in gravity's rainbow

Abstract

When gravitation is combined with quantum theory, the Heisenberg uncertainty principle could be extended to the generalized uncertainty principle accompanying a minimal length. To see how the generalized uncertainty principle works in the context of black hole complementarity, we calculate the required energy to duplicate information for the Schwarzschild black hole. It shows that the duplication of information is not allowed and black hole complementarity is still valid even assuming the generalized uncertainty principle. On the other hand, the generalized uncertainty principle with the minimal length could lead to a modification of the conventional dispersion relation in light of Gravity's Rainbow, where the minimal length is also invariant as well as the speed of light. Revisiting the gedanken experiment, we show that the no-cloning theorem for black hole complementarity can be made valid in the regime of Gravity's Rainbow on a certain combination of parameters.

18 pages, 3 figures, version to appear in JCAP

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Cited by in corpus (7)

• Nonextensive Black Hole Entropy and Quantum Gravity Effects at the Last Stages of Evaporation
• Charged Black Hole in Gravity's Rainbow: Violation of Weak Cosmic Censorship
• GUP and the no-cloning theorem
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• On the reformulation of Thomas-Fermi model to make it compatible to the Planck-scale
• Strong gravitational lensing by black hole in F(R) Euler Heisenberg Gravity's Rainbow
• Gravitational baryogenesis in $F(R)$ gravity's rainbow