Photon Trajectories in the Vicinity of Black Holes

Arnav Reddy Visavaram

Abstract: In this paper, we investigate photon trajectories in the Schwarzschild metric, focusing on how the curvature of spacetime influences the paths of light near a non-rotating, spherically symmetric black hole. The Schwarzschild metric is a solution to Einstein?s field equations that describes a non-rotating spherical black hole. The black hole used in this paper has a mass of one solar mass and a gravitational radius of three kilometers. The photon trajectories are described by a second-order differential equation derived from the geodesic equation for null particles. We solve this equation numerically, simulating the behavior of photons in the strong gravitational field near the black hole. From our simulations, we estimate the opening angle of a cone within which photons can escape to infinity. These results provide insights into the dynamics of photon propagation in curved spacetime and the boundary between capture by the black hole and escape from the black hole, which can be helpful in gravitational lensing, interpreting black hole images and understanding accretion disk emissions. The results confirm the existence of a photon sphere. While this research paper is limited to the Schwarzschild metric, an extension to rotating non-symmetric black holes and inclusion of quantum effects can provide even more insight into astrophysical environments that are more realistic. This work offers a foundation for further research into black hole imaging and relativistic light propagation.

Keywords: Photon trajectories, Black holes, Schwarzschild metric, Photon sphere

How to Cite?: Arnav Reddy Visavaram, "Photon Trajectories in the Vicinity of Black Holes", Volume 15 Issue 6, June 2026, International Journal of Science and Research (IJSR), Pages: 1368-1371, https://www.ijsr.net/getabstract.php?paperid=SR26625233539, DOI: https://dx.doi.org/10.21275/SR26625233539

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