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Generalized 2d-dilaton models, the true black hole and quantum integrability

M. O. Katanaev·W. Kummer·H. Liebl·D. V. Vassilevich
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Abstract

All 1+1 dimensional dipheomorphism-invariant models can be viewed in a unified manner. This includes also general dilaton theories and especially spherically symmetric gravity (SSG) and Witten's dilatonic black hole (DBH). A common feature --- also in the presence of matter fields of any type --- is the appearance of an absolutely conserved quantity C which is determined by the influx of matter. Only for a subclass of generalized dilaton theories the singularity structure vanishes together with C. Such `physical' theories include, of course, SSG and DBH. It seems to have been overlooked until recently that the (classical) 'black hole' singularity of the DBH deviates from SSG in a physically nontrivial manner. At the quantum level for all generalized dilaton theories --- in the absence of matter --- the local quantum effects are shown to disappear. This enables us to compute e.g. the second loop order correction to the Polyakov term. For non-minimal scalar coupling we also believe to have settled the controversial issue of Hawking radiation to infinity with a somewhat puzzling result for the case of SSG.

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M. O. Katanaev, W. Kummer, H. Liebl, D. V. Vassilevich. 1997-09-04. Generalized 2d-dilaton models, the true black hole and quantum integrability. https://arxiv.org/abs/gr-qc/9709010

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