Gravitational Lensing and Tidal Effects of a Planetary Mass Black Hole

This work presents a comprehensive theoretical analysis and numerical calculation of the fundamental physical parameters surrounding a non-rotating, spherically symmetric Schwarzschild black hole. Quantitative Analysis of Schwarzschild Black Hole Spacetime Radius, Light Deflection, Redshift, and Tidal Phenomena. Utilizing General Relativity, to compute the Schwarzschild radius as the defining event horizon. The gravitational time dilation, showing the dramatic slowing of time as the event horizon is approached, and the gravitational redshift of signals emitted from near the horizon. Additionally, this study calculates the relativistic deflection angle of light in the weak-field limit using the geodesic equation. To analyse the structural integrity of objects near the black hole, I have calculated the tidal acceleration and resultant tidal force, demonstrating that tidal stresses approach infinite values at the singularity, causing powerful tidal disruptions and “spaghettification”. Planetary mass black holes have a tiny size and an intense gravitational field to tear apart objects passing nearby their external surface, in contrast to supermassive black holes. These calculations provide a unified model for validating relativistic effects, offering precise quantitative measurements for astrophysical observation. Gravitational time dilation near a black hole is a profound prediction of Einstein’s general relativity, where intense gravity causes time to pass significantly slower for objects closer to the event horizon compared to distant observers. This effect means that an observer near the horizon experiences time as almost frozen from an external viewpoint.