Trouble with geodesics in black-to-white hole bouncing scenarios

TL;DR

This paper examines the behavior of radial timelike geodesics in black-to-white hole bouncing models, revealing issues with geodesic energy loss, horizon proximity, and Planck-scale blueshifts that challenge the scenario's consistency.

Contribution

It provides a detailed analysis of geodesic dynamics in bouncing black hole models, highlighting potential problems with geodesic squeezing and blueshift effects.

Findings

Geodesics lose energy after crossing the transition surface.

Bounded geodesics can be squeezed into the stretched horizon.

Highly squeezed geodesics exhibit Planck-scale blueshift issues.

Abstract

By utilizing the thin shell approximation, we investigate the behavior of radial timelike geodesics in a black hole to white hole bouncing scenario with a mass (de-)amplification relation. We show that those geodesics lose energy after crossing the transition surface if the white hole mass is less than the black hole mass and vice versa. That is, the bounded timelike radial geodesics become closer to the event horizon in the mass decreasing direction. We then show that by tracing a finite amount of bouncing cycles along the mass decreasing direction, all bounded radial geodesics can be squeezed into the range of the stretched horizon while the black hole and white hole are still massive. Those highly squeezed geodesics are problematic since there exists a Planck-scale blueshift between them and the regular infalling trajectories. We also discuss the possible implication and rescues.