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Published January 17, 1994 | Submitted
Journal Article Open

Ultra-Planck scattering in D = 3 gravity theories

Abstract

We obtain the high-energy, small-angle, two-particle gravitational scattering amplitudes in topologically massive gravity (TMG) and its two non-dynamical constituents, Einstein and Chern-Simons gravity. We use 't Hooft's approach, formally equivalent to a leading-order eikonal approximation: one of the particles is taken to scatter through the classical space-time generated by the other, which is idealized to be lightlike. The required geometries are derived in all three models; in particular, we thereby provide the first explicit asymptotically flat solution generated by a localized source in TMG. In contrast to D = 4, the metrics are not uniquely specified, at least by naive asymptotic requirements - an indeterminacy mirrored in the scattering amplitudes. The eikonal approach does provide a unique choice, however. We also discuss the discontinuities that arise upon taking the limits, at the level of the solutions, from TMG to its constituents, and compare with the analogous topologically massive vector gauge field models.

Additional Information

© 1994 Elsevier. Received 1 July 1993, Accepted 30 July 1993. This work was supported by NSF grant PHY88-04561. The research of AS was also supported by SERC at DAMTP, while JM would like to acknowledge the support of the Australian Research Council.

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