Ultra--Planck Scattering in D=3 Gravity Theories

TL;DR

This paper calculates high-energy gravitational scattering amplitudes in three-dimensional topologically massive gravity and related models, providing explicit solutions and analyzing the unique features and indeterminacies of these theories.

Contribution

It derives explicit asymptotically flat solutions in TMG and computes scattering amplitudes using an eikonal approximation, highlighting differences from four-dimensional gravity.

Findings

Explicit solutions in TMG for localized sources

Unique eikonal scattering amplitudes in 3D gravity models

Indeterminacy in asymptotic metrics compared to 4D gravity

Abstract

We obtain the high energy, small angle, 2-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 spacetime 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.