Schwarzschild Black Holes in Extended Spacetime with Two Time Dimensions

Abstract

Black holes are one of the most extreme phenomena in the Universe, bridging the gap between the realms of general relativity and quantum physics. Any matter that crosses the event horizon moves towards the core of the black hole, creating a singularity with infinite mass density—a phenomenon that cannot be comprehended within present theories of relativity and quantum physics. In this study, we undertake an investigation of non-rotating, non-charged Schwarzschild black holes in an extended spacetime framework with two time dimensions. To accomplish this, we extend Einstein’s field equations by one more temporal dimension. We solve the corresponding equations for a spherical central mass, which leads to an Abel-type equation for the 5D Schwarzschild metric. By exploring distinct solution classes, we present an approximate solution for the 5D metric. Our proposed solution maintains consistency with Schwarzschild’s 4D solution. Finally, we address the central black hole singularity and demonstrate a potential breakthrough, as our solution effectively avoids the singularity quandary, providing valuable insight into the fundamental properties of black holes in this augmented framework.