Thermal stability and criticality of quadratic Gaussian space–time

Abstract

The investigation conducted in this study focuses on the phase structure, critical points, and stability of a novel regular pure quadratic Gaussian black hole. Gaussian black holes are a significant category of regular black holes, representing a set of spherically symmetric static solutions derived from Einstein’s equations in the presence of the cosmological constant. The research explores the thermodynamic properties of these black holes within the framework of pure quadratic modified gravity. By applying the laws of black hole thermodynamics, various quantities such as Hawking temperature, equation of state, and Gibbs free energy are analyzed. Moreover, the study examines the phase transitions of such black holes, accompanied by graphical representations of the relevant quantities. Based on the critical points identified, the stability and phase transition behavior of the system are evaluated. The investigation also delves into the assessment of stability, instability, and the Swallowtail behavior exhibited by the system. Also the presence of a discontinuity in the heat capacity leads to a phase transition within the system, reminiscent of Van der Waals-like phase transitions observed between small-large black holes.