Thermodynamics of Einstein–Gauss–Bonnet black holes under the Generalized Uncertainty Principle

We explore the impact of the Generalized Uncertainty Principle (GUP) on the thermodynamics of five-dimensional Einstein–Gauss–Bonnet (EGB) black holes. A modified mass–temperature relation is derived under the assumption of local equilibrium, revealing that the black hole evolves into a stable remnant with a finite temperature, rather than undergoing complete evaporation. The modified entropy, obtained within this framework, deviates from the commonly expected logarithmic form. However, considering a linear GUP, which is obtained by combining Doubly Special Relativity (DSR) with the usual GUP, yields a logarithmic correction to the entropy similar to that of a five-dimensional Schwarzschild–Tangherlini black hole. However, the leading order term in the entropy of the EGB black hole is purely due to the underlying spacetime geometry, making the logarithmic term a higher order correction, unlike the case of the five-dimensional Schwarzschild black hole, where the leading order correction is logarithmic. Our results support the conjecture that the GUP-induced corrections to black hole entropy are sensitive to the dimensionality of spacetime.