TUW-02-15

Virtual Black Holes in Generalized Dilaton Theories

D. Grumiller, W. Kummer, and D.V. Vassilevich

Institut für Theoretische Physik
Technische Universität Wien
Wiedner Hauptstr. 8-10, A-1040 Wien, Austria

Max-Planck-Institut für Mathematik in den Naturwissenschaften,
Inselstr. 22-26, D-04103 Leipzig, Germany

Abstract:

The virtual black hole phenomenon, which has been observed previously in specific models, is established for generic $2D$ dilaton gravity theories with scalar matter. The ensuing effective line element can become asymptotically flat only for two classes of models, among them spherically reduced theories and the string inspired dilaton black hole (CGHS model).

We present simple expressions for the lowest order scalar field vertices of the effective theory which one obtains after integrating out geometry exactly. Treating the boundary in natural and simple way asymptotic states, tree-level vertices and tree-level $S$-matrix are conformally invariant.

Examples are provided pinpointing the physical consequences of virtual black holes on the (CPT-invariant) $S$-matrix for gravitational scattering of scalar particles. For minimally coupled scalars the evaluation of the $S$-matrix in closed form is straightforward.

For a class of theories including the CGHS model all tree-graph vertices vanish, which explains the particular simplicity of that model and at the same time shows yet another essential difference to the Schwarzschild case.

PACS numbers: 04.60.Kz; 04.60.Gw; 11.10.Lm; 11.80.Et