Topological Thermodynamics Imprints Classify Black Hole Critical Points with Charges Q = +1, 0, or -1

Black holes, enigmatic objects predicted by Einstein’s theory, continue to challenge our understanding of gravity and the universe, and recent research delves into the subtle interplay between their thermodynamics and dynamic behaviour. Yue Chu, Chen-Hao Wu, and Ya-Peng Hu from Nanjing University of Aeronautics and Astronautics investigate how fundamental thermodynamic properties leave their imprint on the way black holes evolve. The team classifies critical points within these objects based on their charge, revealing that anomalous black holes in four-dimensional spacetime exhibit all three possible charge states. By analysing the quasinormal modes, essentially the ‘ringing’ of a disturbed black hole, they demonstrate a consistent relationship between a black hole’s radius and its oscillation frequency and damping rate, and importantly, uncover a surprising connection between thermodynamic characteristics and dynamic behaviour across different black hole solutions.

This work demonstrates that all three types of critical points exist within quantum anomalous black holes in four-dimensional spacetime. The team computed the quasinormal modes, which describe vibrations, of massless scalar perturbations near these critical points, finding that both the oscillation frequency and damping rate increase as the black hole radius increases at a critical temperature.

Black Hole Phase Transitions and Thermodynamics

This research investigates the thermodynamic behavior of black holes, exploring how they can undergo phase transitions analogous to those observed in everyday matter. The study connects black hole properties with gravity and employs mathematical tools to understand these complex systems, utilizing the concept of black hole thermodynamics, where black holes are described using concepts like temperature and entropy. The research also explores critical phenomena, unusual behaviors occurring near phase transitions where fluctuations become significant. The authors utilize an extended phase space, treating the cosmological constant as a thermodynamic pressure, to better understand black hole phase transitions and calculate critical exponents, which characterize the behavior of thermodynamic quantities near the critical point. They investigate whether these transitions belong to known universality classes and explore how parameters like charge and cosmological constant affect the phase transition behavior of black holes, extending to higher-dimensional black holes and considering regular black holes as models for more realistic systems.

Topological Charges Classify Black Hole Critical Points

This research successfully classifies critical points in anomalous black holes by associating them with topological charges, revealing a connection between thermodynamics and dynamics. By applying a framework based on Duan’s method and utilizing a vector field constructed from thermodynamic quantities, the team demonstrated the existence of three types of critical points, with charges of +1, 0, and -1, in four-dimensional spacetime. Analysis of quasinormal modes, which describe vibrations, showed that both oscillation frequency and damping rate increase with black hole radius at a critical temperature, a common behavior across all three types of critical points. Notably, the research reveals a consistent dynamical signature for critical points with a charge of -1 across different black hole solutions, suggesting a fundamental link between thermodynamic properties and dynamic behavior. While discernible patterns were not found for the +1 and 0 cases due to limited data, further investigation with a larger dataset is needed to fully understand their behavior. Future work could focus on expanding the analysis to include a wider range of black hole solutions and exploring the implications of these findings for understanding the stability and evolution of black holes in more complex astrophysical scenarios.