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Abstract

Possible quantum extension beyond a black-hole singularity

We look into a semi-classical evaporating 2d black-hole, employing the CGHS model. We construct an approximate analytical solution inside the hole, and explore its (nearly-homogeneous) asymptotic behavior at the singularity. Correspondingly we construct an approximate "near-singularity" effective Hamiltonian H. Next we employ quantum considerations to get clues about the possible extension of space-time beyond the singularity. From H we obtain a Schrodinger-like equation, acting on a wave-function representing the fields' evolution. We solve analytically for the eigen-modes, and use them to construct a localized initial wave-function. After traversing the singularity, the wave-function becomes well-localized again, suggesting the occurrence of a new semi-classical domain beyond the singularity.

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