Thermodynamics and logarithmic corrections of symmergent black holes

In this paper, we study quantum gravity effect on the symmergent black hole which is derived from quadratic-curvature gravity. To do so, we use the Klein-Gordon equation which is modified by generalized uncertainty principle (GUP). After solving the field equations, we examine the symmergent black hole's tunneling and Hawking temperature. We explore the graphs of the temperature through the outer horizon to check the GUP influenced conditions of symmergent black hole stability. We also explain how symmergent black holes behave physically when influenced by quantum gravity. The impacts of thermal fluctuations on the thermodynamics of a symmergent black holes spacetime are examined. We first evaluate the model under consideration's thermodynamic properties, such as its Hawking temperature, angular velocity, entropy, and electric potential. We evaluate the logarithmic correction terms for entropy around the equilibrium state in order to examine the impacts of thermal fluctuations. In the presence of these correction terms, we also examine the viability of the first law of thermodynamics. Finally, we evaluate the system's stability using the Hessian matrix and heat capacity. It is determined that a stable model is generated by logarithmic corrections arising from thermal fluctuations.

Automated summary

In this paper, the researchers investigate the effect of quantum gravity on the symmergent black hole derived from quadratic-curvature gravity. A modified Klein-Gordon equation, incorporating the generalized uncertainty principle (GUP), is used to study the tunneling and Hawking temperature of the symmergent black hole. The stability conditions of the black hole under the influence of GUP are examined by analyzing the temperature graphs near the outer horizon. The impact of thermal fluctuations on the thermodynamics of the black hole spacetime is also analyzed, including the evaluation of logarithmic correction terms for entropy and the viability of the first law of thermodynamics.