Virtual black holes in generalized dilaton theories
Institut für Theoretische Physik, Technische Universität Wien, Wiedner Hauptstr. 8-10, 1040, Wien, Austria
2 Institut für Theoretische Physik, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstr. 22-26, 04103, Leipzig, Germany
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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. 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 a natural and simple way, asymptotic states, tree-level vertices and the 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 string inspired dilation black hole 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.
© Springer-Verlag, 2003