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In this paper, we will generalize the Gauss-Bonnet gravity to an energy-dependent Gauss-Bonnet theory of gravity, which we shall call the Gauss-Bonnet gravity's rainbow. We will also couple this theory to a Maxwell's theory. We will analyze black hole solutions in this energy-dependent Gauss-Bonnet gravity's rainbow. We will calculate the modifications to the thermodynamics of black holes in the Gauss-Bonnet's gravity's rainbow. We will demonstrate that even though the thermodynamics of the black holes get modified in the Gauss-Bonnet gravity's rainbow, the first law of thermodynamics still holds for this modified thermodynamics. We will also comment on the thermal stability of the black hole solutions in this theory.
Hendi et al. (Mon,) studied this question.