Semi-infinite throat as the end-state geometry of two-dimensional black hole evaporation.

We study a modified two-dimensional dilaton gravity theory which is exactly solvable in the semiclassical approximation including back-reaction. The vacuum solutions of this modified theory are asymptotically flat static space-times. Infalling matter forms a black hole if its energy is above a certain threshold. The black hole singularity is initially hidden behind a timelike apparent horizon. As the black hole evaporates by emitting Hawking radiation, the singularity meets the shrinking horizon in finite retarded time to become naked. A natural boundary condition exists at the naked singularity such that for general infalling matter-configurations the evaporating black hole geometries can be matched continuously to a unique static end-state geometry. This end-state geometry is asymptotically flat at its right spatial infinity, while its left spatial infinity is a semi-infinite throat extending into the strong coupling region. ∗ Electronic address: [email protected] ∗∗ Electronic address: [email protected] ∗∗∗ Electronic address: [email protected] Hawking’s discovery that black holes radiate thermally [[1],[2],[3]] gave rise to a longstanding question concerning the consequences of combining quantum theory and general relativity. [[4],[5],[6],[7]] Does evolution from an initial pure state take place unitarily to a final pure state or non-unitarily to a final mixed state? Intimately linked to this question is the final geometry resulting from black hole evaporation. Here we present a specific two-dimensional (2D) dilaton gravity model in which a black hole evaporates leaving a static semi-infinite throat as the end-state or “remnant” geometry. Our model is a modification of the CGHS model.[[8]] We solve the semiclassical equations and get closed-form expressions for the metric and dilaton field. The classical 2D CGHS action [8] is Scl = 1 2π ∫ dx √ −g [ e−2φ ( R + 4(∇φ) + 4λ ) − 1 2 N ∑