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

Understand

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.