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Quantum tunneling and unitarity features of an S-matrix for gravitational collapse

M. Ciafaloni and D. Colferai

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Starting from the semiclassical reduced-action approach to transplanckian scattering by Amati, Veneziano and one of us and from our previous quantum extension of that model, we investigate the S-matrix expression for inelastic processes by extending to this case the tunneling features previously found in the region of classical gravitational collapse. The resulting model exhibits some non-unitary S-matrix eigenvalues for impact parameters b < bc, a critical value of the order of the gravitational radius R = 2Gs1/2, thus showing that some (inelastic) unitarity defect is generally present, and can be studied quantitatively. We find that S-matrix unitarity for b < bc is restored only if the rapidity phase-space parameter y is allowed to take values larger than the effective coupling Gs/hbar itself. Some features of the resulting unitary model are discussed.

Keywords

Black Holes

Classical Theories of Gravity

Models of Quantum Gravity

 

E-print Number: 0909.4523

Cited: by |

Refers: to

PACS

04.60.-m Quantum gravity

03.65.Xp Tunneling, traversal time, quantum Zeno dynamics

02.10.Ud Linear algebra

Subjects

Mathematical physics

Gravitation and cosmology

Quantum information and quantum mechanics

Dates

Issue 12 (December 2009)

Received 1 October 2009, accepted for publication 23 November 2009

Published 22 December 2009



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