Interior design of a two-dimensional semiclassical black hole: Quantum transition across the singularity

Abstract

We study the internal structure of a two-dimensional dilatonic evaporating black hole based on the Callan, Giddings, Harvey, and Strominger model. At the semiclassical level, a (weak) spacelike singularity was previously found to develop inside the black hole. We employ here a simplified quantum formulation of spacetime dynamics in the neighborhood of this singularity, using a minisuperspace-like approach. Quantum evolution is found to be regular and well defined at the semiclassical singularity. A well-localized initial wave packet propagating towards the singularity bounces off the latter and retains its well-localized form. Our simplified quantum treatment thus suggests that spacetime may extend semiclassically beyond the singularity, and also signifies the specific extension.

Approximate solution to the Callan-Giddings-Harvey-Strominger field equations for two-dimensional evaporating black holes

“…(iii) Direct numerical simulations of Hðv; uÞ at various u < u hor values further confirm this conclusion. Summarizing the above discussion on the exact properties of Hðu; vÞ, and briefly restating it in more physical/ geometrical terms: All lines u < u hor make it to FNI, whereas all lines u > u hor run into a spacelike singularity 9 at v ¼ v sing ðuÞ < 0.…”

“…This quantum formulation of the problem seems to resolve the semiclassical singularity inside the BH [8], and thereby to shed new light on the information puzzle. In a very recent paper [9] we applied a more simplified, "Minisuperspace-like", quantum approach to the spacetime singularity inside a CGHS evaporating BH. We obtained a (bounce-like) extension of semiclassical spacetime beyond the singularity.…”

“…H 0 decreases linearly with U, and we only consider here u gauges satisfying du=dU > 0 9. The exact semiclassical CGHS spacetime admits a very similar global structure: A BH, with a spacelike singularity inside it.…”

Black Hole Evaporation: A Perspective from Loop Quantum Gravity

“…Analysis of the fully quantum region is the most difficult of open problems. One promising approach is to generalize the analysis of [61] in which the quantum evolution across the singularity of a 2-dimensional black hole was studied. But the required generalization would be quite non-trivial.…”

Evaporation of two-dimensional black holes

“…In the mean field approximation the extension is ambiguous because of the presence of a singularity along which the metric is C 0 but not C 1 . But it is plausible that these ambiguities will be resolved in the full quantum theory and there is some evidence supporting this expectation [8,26]. What features would this quantum extension have?…”