Entropy relations and GUP corrections of Ernst black hole

Bekenstein bound provides a universal bound on entropy for a black hole that is independent of mass. The universal nature of Entropy and area product of multi-horizon black holes ensure the existence of dual in 2D CFT. So, studying various sums and product relations of thermodynamic quantities, such as entropy. area, Komar energy, etc., for black holes having multiple horizons, has become a trend in quantum gravity. In this paper, we studied the thermodynamic relations of the Ernst black hole. First, we calculated temperature, area, entropy and Komar energies. Then, we derived their sums and products and found that they are not universal except for area. Lastly, we studied thermodynamics with the Generalized Uncertainty Principle (GUP) to verify the effect of the dispersion of space-time on the stability and other behavior of the Ernst black hole.