Avoiding singularities in Lorentzian-Euclidean black holes: the role of atemporality

TL;DR

This paper explores a novel Lorentzian-Euclidean black hole model where atemporality prevents singularities by enabling a signature change across the event horizon, using regularization techniques to solve Einstein's equations.

Contribution

It introduces the concept of atemporality as a dynamical mechanism for signature change in black holes, providing a regularized solution that avoids singularities.

Findings

Signature change occurs at the event horizon.

Atemporality prevents the formation of singularities.

Regularized Kretschmann invariant confirms the regularity.

Abstract

We investigate a Schwarzschild metric exhibiting a signature change across the event horizon, which gives rise to what we term a Lorentzian-Euclidean black hole. The resulting geometry is regularized by employing the Hadamard partie finie technique, which allows us to prove that the metric represents a solution of vacuum Einstein equations. In this framework, we introduce the concept of atemporality as the dynamical mechanism responsible for the transition from a regime with a real-valued time variable to a new one featuring an imaginary time. We show that this mechanism prevents the occurrence of the singularity and, by means of the regularized Kretschmann invariant, we discuss in which terms atemporality can be considered as the characteristic feature of this black hole.