Abstract
We study the motion of thin-shell bubbles and their tunneling in anti de Sitter (AdS) background. We are interested in the case when the outside of a shell is a Schwarzschild-AdS space (false vacuum) and the inside of it is an AdS space with a lower vacuum energy (true vacuum). If a collapsing true vacuum bubble is created, classically it will form a Schwarzschild-AdS black hole. However, this collapsing bubble can tunnel to a bouncing bubble that moves out to spatial infinity. Then, although the classical causal structure of a collapsing true vacuum bubble has the singularity and the event horizon, quantum mechanically the wavefunction has support for a history without any singularity nor event horizon which is mediated by the non-perturbative, quantum tunneling effect. This may be regarded an explicit example that shows the unitarity of an asymptotic observer in AdS, while a classical observer who only follows the most probable history effectively lose information due to the formation of an event horizon.
Highlights
We study the motion of thin-shell bubbles and their tunneling in anti de Sitter (AdS) background
This may be regarded an explicit example that shows the unitarity of an asymptotic observer in AdS, while a classical observer who only follows the most probable history effectively lose information due to the formation of an event horizon
We studied the motion of thin-shell true vacuum bubbles in anti de Sitter background, and discussed the information loss problem
Summary
Where the suffices ± denote the exterior (+) and interior (−) of a thin-shell. The AdS radius l± is related to the vacuum energy density ρ±(< 0) as l2±. If l− < l+, it is a true vacuum bubble, and if l− > l+, it is a false vacuum bubble. We are interested in the case of a true vacuum bubble, so we assume l− < l+. We consider the case when the inside is a pure AdS space (pure true vacuum). We denote the radius of the shell by r. One can express the intrinsic metric on the thin-shell as ds2 = −dt2 + r2(t)dΩ2. Where σ is the surface tension which is assumed to be positive, and ǫ± are the signs of the extrinsic curvature of the shell in the two-dimensional (t, r)-space.
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