Abstract
In the path integral approach, one has to sum over all histories that start from the same initial condition in order to obtain the final condition as a superposition of histories. Applying this into black hole dynamics, we consider stable and unstable stationary bubbles as a reasonable and regular initial condition. We find examples where the bubble can either form a black hole or tunnel toward a trivial geometry, i.e., with no singularity nor event horizon. We investigate the dynamics and tunneling channels of true vacuum bubbles for various tensions. In particular, in line with the idea of superposition of geometries, we build a classically stable stationary thin-shell solution in a Minkowski background where its fate is probabilistically given by non-perturbative effects. Since there exists a tunneling channel toward a trivial geometry in the entire path integral, the entire information is encoded in the wave function. This demonstrates that the unitarity is preserved and there is no loss of information when viewed from the entire wave function of the universe, whereas a semi-classical observer, who can see only a definitive geometry, would find an effective loss of information. This may provide a resolution to the information loss dilemma.
Highlights
We find examples where the bubble can either form a black hole or tunnel toward a trivial geometry, i.e., with no singularity nor event horizon
III, we investigate true vacuum bubbles in asymptotic anti-de Sitter (AdS) and Minkowski backgrounds
We mainly focus on a tunneling channel corresponding to a bouncing solution that results in a trivial geometry without a singularity or an event horizon
Summary
There have been interesting discussions on the information loss problem of black holes [1]. According to Maldacena [7] and Hawking [8], if one of the histories has a trivial topology, namely that there is no horizon nor singularity in the Lorentzian sense, the information will be eventually conserved through the history, even though the probability is suppressed on the order of the entropy This might explain why there is no information loss for the entire wave function of the universe, yet a semi-classical observer, who can see a definite geometry, would effectively detect the loss of information. It might well be that a unitary observer, if any, who lives in the superspace, could approximately describe classical observables as expectation values, where these expectation values do not have to satisfy the classical equations of motion In this sense, there could be a violation of general relativity. Can one technically demonstrate the expectation values of observables in terms of a unitary observer?
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