The ultrarelativistic limit of 2D dilaton gravity and its energy momentum tensor

TL;DR

This paper investigates the ultrarelativistic limit of 2D dilaton gravity, deriving its energy-momentum tensor, analyzing geodesic behavior, and discussing quantization effects, revealing smooth geodesics for minimally coupled particles and finite jumps for non-minimally coupled ones.

Contribution

It provides a detailed derivation of the energy-momentum tensor in the ultrarelativistic limit of 2D dilaton gravity and explores the implications for geodesics and quantum effects.

Findings

Energy-momentum tensor localized on a null line

Smooth geodesics for minimally coupled particles

Finite acceleration jumps for non-minimally coupled particles

Abstract

The ultrarelativistic limit of twodimensional dilaton gravity is presented and its associated (anti-)selfdual energy momentum tensor is derived. It is localized on a null line, although the line element remains twice differentiable. Relations to the Aichelburg-Sexl spacetime and constant dilaton vacua are pointed out. Geodesics are found to be smooth for minimally coupled test particles but non-smooth -- with a finite jump in the acceleration -- for test particles coupled non-minimally to the dilaton. Quantization on boosted backgrounds is discussed; no anomalous trace of the energy momentum tensor arises and the 1-loop flux component can be adjusted to be equal to the classical flux of the shock wave.