Complex Riemannian spacetime and singularity-free black holes and cosmology

TL;DR

This paper introduces a complex Riemannian spacetime method to regularize black hole and cosmological singularities, providing singularity-free solutions that could bridge classical and quantum gravity.

Contribution

It presents a novel complex extension technique to remove singularities in black hole and cosmological models, enabling regular solutions without full quantum gravity.

Findings

Regularized Schwarzschild and Kerr black holes

Singularity-free Big Bang cosmology with bounce

Potential link between classical GR and quantum effects

Abstract

An approach is presented to address singularities in general relativity using a complex Riemannian spacetime extension. We demonstrate how this method can be applied to both black hole and cosmological singularities, specifically focusing on the Schwarzschild and Kerr black holes and the Friedmann-Lema\^itre-Robertson-Walker (FLRW) Big Bang cosmology. By extending the relevant coordinates into the complex plane and carefully choosing integration contours, we show that it is possible to regularize these singularities, resulting in physically meaningful, singularity-free solutions when projected back onto real spacetime. The removal of the singularity at the Big Bang allows for a bounce cosmology. This approach offers a potential bridge between classical general relativity and quantum gravity effects, suggesting a way to resolve longstanding issues in gravitational physics without requiring a full theory of quantum gravity.