Thermodynamics of the Magnetic Black Hole in Four-Dimensional ESTGB Theory and Quantum Correction

In this paper, we ascertain the temperature and entropy of the magnetic black hole in four-dimensional ESTGB theory, and investigate the effects of generalized uncertainty principle (GUP) on standard thermodynamics of this black hole. For this purpose, we derive Hawking radiation for scalar particles and fermions in tunneling formalism by applying the Hamilton-Jacobi method and the semiclassical WKB approximation. We evalute the corrected thermodynamics quantities of the magnetic black hole to explore how the effect of quantum gravity changes the thermodynamic properties and evaporation of the black hole. We find logarithmic correction of the black hole entropy, remnants and phase transition phenomena of the black hole are also observed at the end of evaporation. The results show that GUP plays a important role in the end stage of the black hole evaporation. In addition, we compare the thermodynamic properties of the magnetic black hole and Reissner-Nordstrom (RN) black hole under the influence of GUP.

Automated summary

This paper investigates the temperature and entropy of a magnetic black hole in the four-dimensional ESTGB theory and explores the effects of generalized uncertainty principle (GUP) on its standard thermodynamics. The study reveals that GUP plays an important role in the final stage of black hole evaporation, with observed logarithmic correction of entropy, remnants, and phase transition phenomena.