Theoretical and Mathematical Examination of Black Hole Spacetime Dynamics

Abstract

Black holes represent one of the most profound predictions of Einstein's general theory of relativity, constituting regions of spacetime where gravitational effects become so extreme that nothing, including light, can escape. This review paper examines the theoretical and mathematical frameworks underlying black hole spacetime dynamics, synthesizing contemporary research on metric solutions, singularity theorems, and horizon properties. The primary objectives include analyzing Schwarzschild and Kerr metric formulations, evaluating Penrose-Hawking singularity theorems, and examining thermodynamic properties of black hole horizons. The methodology employs systematic literature review of peer-reviewed publications from Google Scholar, focusing on mathematical physics approaches to spacetime geometry. The hypothesis posits that unified mathematical treatment of black hole dynamics reveals fundamental connections between general relativity, quantum mechanics, and thermodynamics. Results demonstrate significant advances in understanding event horizon mathematics, geodesic equations, and Hawking radiation mechanisms. Discussion reveals that black hole spacetime dynamics remain central to theoretical physics, with implications for quantum gravity research. The conclusion emphasizes the necessity of continued mathematical investigation for resolving information paradox and singularity problems in black hole physics.