Quantum-Corrected Thermodynamics of Conformal Weyl Gravity Black Holes: GUP Effects and Phase Transitions

Abstract

We investigate the thermodynamic properties of black holes in Conformal Weyl Gravity (CWG) using the Mannheim-Kazanas solution, with particular emphasis on quantum corrections that become significant near the Planck scale. Our analysis employs the Hamilton-Jacobi tunneling formalism to derive the Hawking temperature, revealing explicit contributions from the conformal parameters $\beta$, $\gamma$, and $k$ that lead to substantial deviations from the behavior of a Schwarzschild black hole. We incorporate quantum gravitational effects through the Generalized Uncertainty Principle, demonstrating systematic suppression of thermal radiation in the near-Planckian regime. Using an exponentially corrected entropy model, we compute the complete spectrum of QC thermodynamic potentials, including internal energy, pressure, heat capacity, and free energies. Our heat capacity analysis shows divergence behavior that separates stable and unstable regions, indicating possible thermodynamic transitions controlled by the scale-dependent parameter $\gamma$. The Joule-Thomson expansion analysis shows distinct cooling and heating regimes with inversion points that shift systematically with CWG parameters, capturing QC phase transitions absent in general relativity. We also examine gravitational redshift in CWG geometry, finding complex radial dependence that highlights modifications compared to the Schwarzschild case, although redshift alone cannot observationally distinguish CWG from Einstein's theory. Our results demonstrate that CWG offers a consistent framework for studying black hole thermodynamics beyond general relativity, with quantum corrections modifying phase structures in the near-Planckian regime, though these effects are not expected to yield direct observational consequences.

23 pages, 13 figures, and 4 tables. Published version

References in corpus (19)

• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• Quantum-corrected black hole thermodynamics to all orders in the Planck length
• Joule-Thomson Expansion of Charged AdS Black Holes
• Hawking Radiation as Quantum Tunneling from Noncommutative Schwarzschild Black Hole
• Modified theories of Gravity: Why, How and What?
• The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field
• General class of wormhole geometries in conformal Weyl gravity
• Solution to the ghost problem in fourth order derivative theories
• Minimal Length and Bouncing Particle Spectrum
• Exponential corrections to black hole entropy
• Quantum Gravitational Corrections to the Entropy of a Schwarzschild Black Hole
• Counting black hole microscopic states in loop quantum gravity
• Conformal Weyl gravity and perihelion precession
• Joule-Thomson expansion of Lower-dimensional black hole
• Magnetically charged AdS black holes and Joule-Thomson expansion
• Thermodynamics of Einstein-Euler-Heisenberg Black Holes with Thermal Fluctuations and Nonlinear Electromagnetic Fields
• Nonlinear Einstein-Power-Yang-Mills AdS Black Holes: From Quantum Tunneling to Aschenbach Effect
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Test of conformal gravity as an alternative to dark matter from the observations of elliptical galaxies