A Study on Black Hole Thermodynamics in Classical and Modified Gravity Frameworks

Abstract

Black hole thermodynamics serves as a profound intersection of general relativity, quantum newlinemechanics, and statistical physics, offering deep insights into the fundamental nature of gravity and the structure of spacetime. This thesis presents a comprehensive investigation into the thermodynamic behavior of black holes within both classical and modified gravity frameworks. We explore key thermodynamic quantities such as entropy, temperature, heat capacity, and free energy associated with a variety of static and dynamic black hole solutions. newlineOur study begins with the classical perspective, particularly within the framework of Einstein s general relativity, where we revisit foundational thermodynamic relations and examine their implications in cosmological contexts. Extending beyond the classical domain, we delve into several modified theories of gravity to assess how deviations from Einstein s theory influence black hole thermodynamics. These alternative theories introduce corrections to conventional thermodynamic quantities, potentially offering resolutions to longstanding puzzles such as the information paradox and singularity issues. newlineFurthermore, we analyze the role of black holes as thermodynamic systems by modeling them as working substances in holographic heat engine cycles. The efficiency of these engines, constructed using both classical and modified black hole metrics, is calculated and tested against the laws of thermodynamics. Our findings reveal novel behavior in the presence of modified gravity terms and provide a broader understanding of energy extraction processes in strong gravity regimes. newlineIn summary, the thesis presents a comprehensive study of black hole physics through the lens of both classical and modified theories of gravity and their diverse cosmological implications, deepening our understanding of these enigmatic objects and providing significant insights for future exploration. newline