Towards an S-matrix Description of Gravitational Collapse

Abstract

Extending our previous results on trans-Planckian ($Gs\gg \hslash$) scattering of light particles in quantum string-gravity we present a calculation of the corresponding S-matrix from the region of large impact parameters ($b\gg G\sqrt{s}>{\lambda }_s$) down to the regime where classical gravitational collapse is expected to occur. By solving the semiclassical equations of a previously introduced effective-action approximation, we find that the perturbative expansion around the leading eikonal result diverges at a critical value $b=b_c=O(G\sqrt{s})$, signalling the onset of a new (black-hole related?) regime. We then discuss the main features of our explicitly unitary S-matrix -- and of the associated effective metric -- down to (and in the vicinity of) $b=b_c$, and present some ideas and results on its extension all the way to the $b\to 0$ region. We find that for $b<b_c$ the physical field solutions are complex-valued and the S-matrix shows additional absorption, related to a new production mechanism. The field solutions themselves are, surprisingly, everywhere regular, suggesting a quantum-tunneling -- rather than a singular-geometry -- situation.

39 pages, 5 figures; added discussion sect. 7, added references, acknowledgements

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