Black Hole Thermodynamics in Harada's inspired theory of gravity: Stability, Phase Structure and Geometrothermodynamics

Abstract

In this paper, we investigate the thermodynamic properties of spherically symmetric, static black hole solutions within the framework of Conformal Killing Gravity (CKG). This is a modified theory of gravity that retains all solutions of General Relativity, while addressing some of its theoretical shortcomings and enriching gravitational phenomenology at large distances. We derive key thermodynamic quantities, including mass, temperature, heat capacity and Gibbs free energy, to examine the stability and phase structure of extended Schwarzschild-AdS and charged AdS black holes. Furthermore, employing the formalism of geometrothermodynamics, we analyze the behavior of the thermodynamic curvature scalar to identify critical points and characterize phase transitions. Our results demonstrate that the parameter \( λ\), which quantifies deviations from Einstein's theory, plays a pivotal role in shaping the thermodynamic behavior, resulting in new stability conditions and distinct phase transition patterns compared to those predicted by standard General Relativity.

13 pages; 14 figures

References in corpus (13)

• Dark Energy and the Accelerating Universe
• Dark Matter Candidates from Particle Physics and Methods of Detection
• The Generalized Uncertainty Principle in (A)dS Space and the Modification of Hawking Temperature from the Minimal Length
• Geometrothermodynamics of black holes
• Effects of dark energy on P-V criticality of charged AdS black holes
• Critical phenomena of static charged AdS black holes in conformal gravity
• Critical behaviour and microscopic structure of charged AdS black holes via an alternative phase space
• Emergence of the Cotton tensor for describing gravity
• Can Hawking temperatures be negative ?
• Cotton gravity and 84 galaxy rotation curves
• Consistency Problems of Conformal Killing Gravity
• Tolman-Oppenheimer-Volkoff equation and static spheres in Conformal Killing gravity
• Vanishing of Conserved Charges in Cotton Gravity

Cited by in corpus (4)

• Confronting dark energy in Harada's Conformal Killing Gravity with observational data
• Topological Signatures and Geometrothermodynamics of Critical Phenomena in Regularized Maxwell Black Holes
• Thermodynamics and information recovery of Schwarzschild AdS black holes in conformal Killing gravity
• Thermodynamic formulation of Cotton gravity in the Codazzi parametrization