Free-fall Frame Black Hole in Gravity's Rainbow

Abstract

Doubly special relativity (DSR) is an effective model for encoding quantum gravity in flat spacetime. To incorporate DSR into general relativity, one could use "Gravity's rainbow", where the spacetime background felt by a test particle would depend on its energy. In this scenario, one could rewrite the rainbow metric $g_{\mu \nu }\left(E\right)$ in terms of some orthonormal frame fields and use the modified equivalence principle to determine the energy dependence of $g_{\mu \nu }\left(E\right)$. Obviously, the form of $g_{\mu \nu }\left(E\right)$ depends on the choice of the orthonormal frame. For a static black hole, there are two natural orthonormal frames, the static one hovering above it and freely falling one along geodesics. The cases with the static orthonormal frame have been extensively studied by many authors. The aim of this paper is to investigate properties of rainbow black holes in the scenario with the free-fall orthonormal frame. We first derive the metric of rainbow black holes and their Hawking temperatures in this free-fall scenario. Then, the thermodynamics of a rainbow Schwarzschild black hole is studied. Finally, we use the brick wall model to compute the thermal entropy of a massless scalar field near the horizon of a Schwarzschild rainbow black hole in this free-fall scenario.

18 pages, 2 figures, Journal version. arXiv admin note: substantial text overlap with arXiv:1507.03768

References in corpus (9)

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• Effect of Snyder-de Sitter model on the Black hole thermodynamics in the context of rainbow gravity
• Imperfect fluid cosmological model in modified gravity
• Black holes in multi-fractional and Lorentz-violating models
• The thermodynamics and phase transition of a rainbow black hole
• On the Quantization of the Charge-Mass Ratio
• Free-fall Rainbow BTZ Black Hole
• Exploring black hole mechanics in cotangent bundle geometries
• Thermodynamics and Phase transition of Schwarzschild black hole in Gravity's Rainbow