Quantum tunneling of fermions from kerr-like black holes within topologically massive gravity

In the framework of 3-D general relativity, this study explores a Kerr-like black hole solution with a focus on its causal structure and particle dynamics, employing Penrose diagrams to elucidate the spacetime geometry. The research investigates the behavior pf particles in the vicinity of the event horizon, analyzing their trajectories and potential fates, including the influence of the black hole’s rotation and gravitational effects. The Dirac equation is solved in this curved spacetime using “WKB approximation”, allowing the computation of the Hawking temperature and unveiling quantum effects associated with black hole geometries in three dimensions. Moreover, the phenomenon of superradiance is explored, highlighting the mechanisms through with the rotational energy and angular momentum of the black hole are extracted. This phenomenon provides deeper insights into energy transfer processes and the stability of such black hole solutions. The research contributes to a better understanding of black hole thermodynamics, particularly in lower-dimensional gravitational settings, and offers a comprehensive analysis of energy exchange processes. By integrating classical and quantum perspectives, this study enhances the comprehension of particle dynamics, quantum field behavior, and thermodynamic properties of black holes, enriching the broader field of lower-dimensional gravitational models and their implications for fundamental physics.