Thermodynamics of BTZ Black Holes in Gravity's Rainbow

Abstract

In this paper, we deform the thermodynamics of a BTZ black hole from rainbow functions in gravity's rainbow. The rainbow functions will be motivated from results in loop quantum gravity and Noncommutative geometry. It will be observed that the thermodynamics gets deformed due to these rainbow functions, indicating the existence of a remnant. However, the Gibbs free energy does not get deformed due to these rainbow functions, and so the critical behaviour from Gibbs does not change by this deformation.This is because the deformation in the entropy cancel's out the temperature deformation.

22 pages, 8 figures, added references, corrected typos

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• Dark Energy Star in Gravity's Rainbow
• Thermodynamics of Reissner-Nordström Black Holes in Higher Dimensions: Rainbow Gravity Background With General Uncertainty Principle
• Quantum corrections to the thermodynamics of rotating charged BTZ black hole in gravity's rainbow
• Quantum-corrected Schwarzschild AdS black hole surrounded by quintessence: Thermodynamics and Shadows
• New black hole solutions in three-dimensional $f(R)$ gravity
• Three-dimensional AdS black holes in massive-power-Maxwell theor
• Adiabatic analysis of the rotating BTZ black hole
• Free-fall Rainbow BTZ Black Hole