Spacetime surgery for black hole fireworks

Abstract

We construct an explicit model for the black hole to white hole transition (known as the black hole fireworks scenario) using the cut-and-paste technique. We model a black hole collapse using the evolution of a time-like shell in the background of the loop quantum gravity inspired metric and then the space-like shell analysis to construct the firework geometry. Our simple and well-defined analysis removes some subtle issues that were present in the previous literature [1] and makes the examination of the junction conditions easier. We further point out that the infalling and asymptotic observers, both in ours and the original scenario in ref. [1], encounter quite different physics. While the proper time of the bounce for an infalling observer can be determined without ambiguity, the bouncing time interval for the asymptotic observer can be chosen arbitrarily by changing how one cuts and pastes the spacetimes outside the event horizons. It is puzzling that the proper time of a distant (rather than infalling) observer is subject to randomness since the infalling observer is supposed to experience a stronger quantum gravity effect. This result might suggest that a black hole firework scenario does not allow for the existence of an effectively classical spacetime inside the horizon. The main message is therefore that even if we strictly follow the thin shell formalism to cut and paste spacetimes, this does not guarantee that the resulting spacetime offers a physically reasonable background.