Revisiting the Schwarzschild black hole solution: A distributional approach

Abstract

We present a novel perspective on the Schwarzschild, Reissner–Nordstrom, and Massless Black Holes solutions, a cornerstone of general relativity, by employing a distributional approach. The conventional solutions are shown to be incomplete, failing to capture the true nature of the gravitational field near the black hole’s singularity. Drawing from advanced concepts in functional analysis and distribution theory, we derive generalized solutions that resolves the apparent singularities and provides new insights into the behavior of matter and energy in the vicinity of a black hole. Our findings suggest the possibility of quantum tunneling, allowing particles to traverse the event horizon under specific conditions. This work not only offers a more rigorous treatment of the Schwarzschild, Reissner–Nordstrom and Massless Black Hole solutions but also paves the way for a deeper understanding of black hole physics and the interplay between general relativity and quantum mechanics.