Title: 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.