On the geometry of the black-to-white hole transition within a single asymptotic region

TL;DR

This paper presents an explicit Lorentzian metric describing a singularity-free black-to-white hole transition within the same asymptotic region, incorporating quantum corrections and detailed geometric analysis.

Contribution

It provides the first explicit metric for a black-to-white hole transition in a single asymptotic region, combining classical and quantum geometry with detailed parameterization.

Findings

The metric smoothly interpolates between black and white horizons.

Quantum corrections are incorporated via loop-quantum-cosmology techniques.

The transition process is characterized by a global geometrical parameter.

Abstract

We write explicitly the complete Lorentzian metric of a singularity-free spacetime where a black hole transitions into a white hole located in its same asymptotic region. In particular, the metric interpolates between the black and white horizons. The metric satisfies the Einstein field equations up to the tunneling region. The matter giving rise to the black hole is described by the Oppenheimer-Snyder model, corrected with loop-quantum-cosmology techniques in the quantum region. The interior quantum geometry is fixed by a local Killing symmetry, broken at the horizon transition. At large scale, the geometry is determined by two parameters: the mass of the hole and the duration of the transition process. The latter is a global geometrical parameter. We give the full metric outside the star in a single coordinate patch.