Validating the Scale Invariance of Time Dilation Factor as Function of Radial Distance from The Blackhole

This paper studies the scale invariance of the gravitational time dilation graph near the Schwarzschild radius (Rs), based on the graphical analysis presented by Abheek Panigrahi. Using the gravitational time dilation equation, we analyse the behaviour of the curve as r approaches Rs. The study validates the scale-invariant nature of the graph by comparing normalized plots for several known black holes with different masses and Schwarzschild radii. The results show that, when scaled with respect to Rs, the overall behavior of the time dilation curve remains consistent across different black holes, demonstrating a universal relativistic pattern near the event horizon.