Quantum Gravity Study Defines Restricted Phase Space Thermodynamics For Charged Rotating Black Holes

Black holes present a unique laboratory for exploring the fundamental connections between gravity, theory and statistical mechanics, and scientists continually seek new ways to test the limits of Einstein’s theory. Amijit Bhattacharjee and Prabwal Phukon, from Dibrugarh University, along with their colleagues, investigate a newly developed approach called restricted phase space thermodynamics, applying it to charged, static and rotating black holes within a modified theory of gravity. This research distinguishes itself by keeping the cosmological constant fixed, introducing a central charge and its associated chemical potential, which allows for a consistent interpretation of black hole mass as internal energy. The team’s analysis reveals characteristics of both first and second-order phase transitions, and importantly, confirms a geometric correspondence between curvature singularities and specific heat capacity divergences, demonstrating the power of this new thermodynamic framework to capture black hole criticality in modified gravity theories.

Scientists investigate how black holes behave when gravity deviates from Einstein’s general relativity, focusing on modifications involving the Ricci scalar. The study employs restricted phase space thermodynamics, a method for detailed analysis of black hole criticality and potential phase transitions, and geometrothermodynamics, a geometric approach using curvature to characterize thermodynamic interactions. Building upon established connections between black hole event horizons and thermodynamic properties like entropy and temperature, scientists aim to uncover novel behaviours and gain a deeper understanding of black hole thermodynamics in these modified gravity scenarios. The team demonstrates that these methods successfully reveal critical points and phase transitions, analogous to those observed in ordinary matter, providing insights into the fundamental nature of gravity and black holes.

Modified Gravity Black Hole Phase Transitions

This study pioneers the application of restricted phase space thermodynamics (RPST) to charged static and rotating black holes within modified gravity theories, specifically f(R) gravity. Unlike conventional approaches, RPST maintains a fixed cosmological constant and introduces a central charge, allowing for a consistent interpretation of black hole mass as internal energy. Researchers derived key thermodynamic quantities and analysed temperature-entropy and Helmholtz free energy-temperature behaviours to identify characteristics of both first and second-order phase transitions, evidenced by non-monotonic curves and swallow-tail structures. To validate these findings, scientists employed geometrothermodynamics (GTD), a method that describes thermodynamic systems using differential geometry. The team demonstrated a precise correspondence between curvature singularities in the GTD scalar curvature and divergences in specific heat capacity curves, establishing a geometric link to phase transitions. This involved complex numerical analysis due to the two parameters present in the charged rotating black hole system, which researchers addressed by introducing a dimensionless parameter to simplify the analysis.

Black Hole Phase Transitions in Modified Gravity

Scientists have systematically explored restricted phase space thermodynamics (RPST) within the framework of f(R) gravity, extending this approach to modified gravity theories for the first time. This work investigates charged static and charged rotating black holes, revealing rich phase structures and critical phenomena not previously observed in this context. The team demonstrated that the black hole mass can be consistently interpreted as internal energy within RPST, simplifying the analysis of thermodynamic processes. Experiments revealed characteristic features of first-order phase transitions in both charged static and rotating black holes, evidenced by non-monotonic curves in temperature-entropy diagrams and swallow-tail profiles in free energy-temperature plots. To validate these findings, scientists employed geometrothermodynamics (GTD), demonstrating a precise correspondence between curvature singularities in the GTD scalar curvature and divergences in specific heat capacity. This geometric correspondence provides further support for the robustness of RPST in capturing black hole criticality within modified gravity theories.

F(R) Gravity and Black Hole Thermodynamics

This research presents a systematic investigation of restricted phase space thermodynamics (RPST) applied to charged static and rotating black holes within the framework of f(R) gravity. Researchers demonstrated that RPST remains a consistent and predictive approach even when considering modifications to Einstein’s general relativity, specifically through the inclusion of higher-order curvature corrections present in f(R) gravity. Analysis of thermodynamic quantities for charged static black holes revealed first-order phase transitions, evidenced by non-monotonic temperature-entropy curves and swallow-tail structures in free energy-temperature plots. For charged rotating black holes, while analytical solutions proved challenging, careful numerical analysis identified scaling relations and critical quantities, again confirming the presence of both first and second-order phase transitions. To further validate these thermodynamic findings, the team employed geometrothermodynamics (GTD), establishing a clear correspondence between curvature singularities in GTD scalar curvature and divergences in specific heat capacity. Overall, this research demonstrates that RPST provides a conceptually sound and mathematically consistent framework for analysing black hole thermodynamics in f(R) gravity, suggesting it captures universal aspects of black hole behaviour independent of the underlying gravitational theory.