# Thermodynamics and logarithmic corrections of symmergent black holes

## TL;DR

This paper investigates quantum gravity effects on symmergent black holes derived from quadratic-curvature gravity, analyzing thermodynamics, stability, and the impact of thermal fluctuations with logarithmic entropy corrections.

## Contribution

It introduces a detailed analysis of quantum gravity effects on symmergent black holes, including thermodynamic properties and stability under thermal fluctuations with logarithmic corrections.

## Key findings

- Logarithmic corrections improve black hole stability.
- Quantum gravity influences thermodynamic behavior.
- Thermal fluctuations affect entropy and stability.

## Abstract

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.