The virtual black hole in 2d quantum gravity

Details The virtual black hole in 2d quantum gravity The virtual black hole in 2d quantum gravity

2000-01-14

arxiv.org/abs/gr-qc/0001038v1

Nucl.Phys. B580 (2000) 438-456

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, 3 figures

Scientific paper

10.1016/S0550-3213(00)00231-5

As shown recently (W. Kummer, H. Liebl, D.V. Vassilevich, Nucl. Phys. B 544, 403 (1999)) 2d quantum gravity theories --- including spherically reduced Einstein-gravity --- after an exact path integral of its geometric part can be treated perturbatively in the loops of (scalar) matter. Obviously the classical mechanism of black hole formation should be contained in the tree approximation of the theory. This is shown to be the case for the scattering of two scalars through an intermediate state which by its effective black hole mass is identified as a ``virtual black hole''. The present discussion is restricted to minimally coupled scalars without and with mass. In the first case the probability amplitude diverges, except the black hole is ``plugged'' by a suitable boundary condition. For massive scalars a finite S-matrix element is obtained.

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