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