Local free-fall Temperature of modified Schwarzschild black hole in rainbow spacetime

Abstract

We obtain a (5+1)-dimensional global flat embedding of modified Schwarzschild black hole in rainbow gravity. We show that local free-fall temperature in rainbow gravity, which depends on different energy $\omega$ of a test particle, is finite at the event horizon for a freely falling observer, while local temperature is divergent at the event horizon for a fiducial observer. Moreover, these temperatures in rainbow gravity satisfy similar relations to those of the Schwarzschild black hole except overall factor $g(\omega )$, which plays a key role of rainbow functions in this embedding approach.

12 pages, 4 figures, version to appear in MPLA

References in corpus (9)

• Planck-scale modified dispersion relations and Finsler geometry
• Absence of Black Holes at LHC due to Gravity's Rainbow
• Modified (A)dS Schwarzschild black holes in Rainbow spacetime
• Rainbow universe
• Covariant anomaly and Hawking radiation from the modified black hole in the rainbow gravity theory
• Thermodynamic phase transition in the rainbow Schwarzschild black hole
• Black Hole Complementarity in Gravity's Rainbow
• The kinematics of particles moving in rainbow spacetime
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Cited by in corpus (7)

• Thermodynamic stability of modified Schwarzschild-AdS black hole in rainbow gravity
• Effect of Snyder-de Sitter model on the Black hole thermodynamics in the context of rainbow gravity
• Hawking, Fiducial, and Free-fall Temperatures of Black Hole on Gravity's Rainbow
• GEMS embeddings and freely falling temperatures of Schwarzschild(-AdS) black holes in massive gravity
• Local free-fall temperatures of charged BTZ black holes in massive gravity
• Rainbow Rindler metric and Unruh effect
• GEMS embeddings of Schwarzschild and RN black holes in Painlevé-Gullstrand spacetimes