Solving the Geodesic Equations for Photon in Schwarzschild, Kerr, and Kerr-Schild Blackhole Spacetime for Estimating Light Propagation

Banerjee, Namrata (2025) Solving the Geodesic Equations for Photon in Schwarzschild, Kerr, and Kerr-Schild Blackhole Spacetime for Estimating Light Propagation. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Namrata Banerjee (20MS123)) 20MS123_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (732kB)

Abstract

This project investigates the behavior of photon trajectories in curved spacetime by solving the geodesic equations in three black hole metrics: Schwarzschild, Kerr, and Kerr-Schild. These metrics correspond respectively to non-rotating and rotating black holes, with the Kerr-Schild form allowing for simplified numerical treatment of rotating solutions. The equations of motion for massless particles (photons) are derived using the variational principle and expressed in terms of first-order differential equations. We employ the classical fourth-order Runge-Kutta (RK4) method for numerical integration of these equations under various initial conditions. The resulting photon paths are analyzed and visualized to gain insight into gravitational lensing, light bending, and the influence of spacetime rotation on photon dynamics. This study not only enhances understanding of General Relativity in strong gravity regimes but also contributes toward computational tools relevant for astrophysical modeling, including black hole imaging

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