An alternative approach to the static spherically symmetric vacuum global solution to the Einstein's equations

TL;DR

This paper introduces a novel approach to describing Schwarzschild black holes by enforcing staticity inside the horizon, leading to a signature change and symmetry transition at the horizon, with implications for test particle motion.

Contribution

It presents an alternative solution to the Schwarzschild black hole by requiring staticity inside the horizon, resulting in a signature change and symmetry transition not present in standard solutions.

Findings

Signature change at the horizon R=2m.

Symmetry transition across the horizon.

Altered test particle dynamics due to the new solution.

Abstract

We propose an alternative description of the Schwarzschild black hole based on the requirement that the solution be static not only outside the horizon but also inside it. As a consequence of this assumption, we are led to a change of signature implying a complex transformation of an angle variable. There is a "phase transition" on the surface R=2m, producing a change in the symmetry as we cross this surface. Some consequences of this situation on the motion of test particles are investigated.