Simpson-visser Black Hole Study Reveals Discontinuous Heat Capacity, Refining Quantum Entropy for Regular Spacetimes

Regular black holes represent a crucial step towards resolving the problematic singularities at the heart of standard black hole theory, and Vinayak Joshi from the Indian Institute of Technology Roorkee, along with Ashok B. Joshi from the International Center for Cosmology, Charusat University, and their colleagues, have investigated the thermodynamic properties of one such model, the Simpson-Visser “black-bounce” geometry. Their work reveals a critical instability within this regular spacetime, identified by a distinct discontinuity in the heat capacity, which indicates a fundamental shift in how the black hole evaporates and is influenced by the parameters defining its regularity. Extending beyond conventional calculations, the team also derives quantum corrections to the black hole’s entropy using a sophisticated tunneling approach, providing a more accurate statistical description of these non-singular spacetimes. These findings demonstrate that resolving the singularity isn’t simply a geometric fix, but a significant thermodynamic event with important consequences for understanding the stability and ultimate fate of evaporating black holes.

Regular Black Holes and Quantum Thermodynamics

The study of black holes continues to push the boundaries of theoretical physics, particularly in the quest to reconcile general relativity with quantum mechanics. Scientists are increasingly focused on exploring black hole solutions that move beyond the standard models, investigating regular black holes that lack the central singularity predicted by classical theory. These regular black holes often incorporate modified gravity theories or require the presence of exotic matter, prompting research into their thermodynamic properties, including entropy, temperature, and heat capacity. A key area of investigation involves understanding phase transitions within black holes and how these transitions might be affected by quantum effects.,.

Simpson-Visser Geometry Resolves Central Singularity

Scientists are employing the Simpson-Visser geometry as a framework to explore how singularities at the heart of black holes can be resolved. This geometry, defined by a specific mathematical structure incorporating a parameter that controls regularization, prevents the formation of a singularity at the center. Calculations confirm that all measures of curvature remain finite throughout the spacetime, explicitly demonstrating the absence of a singularity, even at the core. Researchers meticulously analyze the causal structure, identifying horizons and categorizing the spacetime based on the relationship between the regularization parameter and the black hole’s mass. To understand the physical source supporting this geometry, the team investigates the stress-energy tensor, revealing that exotic matter is necessary to maintain the regular spacetime. They then compute fundamental thermodynamic properties, such as Hawking temperature and Bekenstein-Hawking entropy, establishing a baseline for further investigation of stability and quantum corrections.,.

Regular Black Hole Instability and Critical Points

This work presents a detailed thermodynamic analysis of regular black holes, specifically utilizing the Simpson-Visser geometry. Scientists demonstrate that this regular spacetime exhibits a critical instability, pinpointing a discontinuity in the heat capacity that signals a fundamental change in the black hole’s evaporation state. The location of this critical point is directly dependent on the regularization parameter, which governs the geometry’s transition between a standard black hole and a wormhole. Researchers probe thermodynamic stability beyond standard calculations, focusing on heat capacity and free energy as functions of the regularization parameter.

The analysis reveals a critical point where the heat capacity diverges, indicating a second-order phase transition within the black hole’s structure. This transition signifies a profound alteration in the black hole’s behavior as it evaporates, directly linked to the resolution of the central singularity. Pushing beyond the semiclassical approximation, the team derives leading-order quantum corrections to the entropy using the Hamilton-Jacobi tunneling formalism. These calculations provide a refined statistical basis for understanding the entropy of non-singular spacetimes and offer a quantitative analysis of the black hole’s end-state.,.

Singularity Resolution Stabilizes Black Hole Thermodynamics

This research presents a detailed thermodynamic and quantum analysis of regular black holes, specifically employing the Simpson-Visser spacetime as a model for singularity resolution. The team discovered a critical instability within this spacetime, manifesting as a phase transition at a specific regularization scale. This transition demarcates a shift from an unstable thermodynamic state, similar to a standard black hole, to a stable equilibrium, a state impossible for singular black holes. Further investigation into free energy revealed a minimum value at zero regularization, suggesting a fundamental restructuring of the black hole’s thermodynamic properties through singularity resolution.

The study extends beyond the semiclassical limit, deriving corrections to black hole entropy using the Hamilton-Jacobi tunneling formalism. These calculations demonstrate that the resolution of the singularity is not merely a geometric modification, but a significant thermodynamic event with measurable consequences for the black hole’s stability and ultimate fate. The results indicate that the final state of an evaporating black hole is a stable, non-singular configuration possessing a non-zero logarithmic entropy determined by the quantum gravity scale. The authors acknowledge that their analysis relies on specific approximations and that further research is needed to explore the full implications of these findings. Future work could investigate the robustness of these results with different regularization schemes and explore the connection to potential observational signatures of stable black hole remnants.