Particle dynamics in a class of 2-dimensional gravity theories

TL;DR

This paper introduces a method to determine the trajectories of classical particles in various 2D gravity theories, including notable models like CGHS and JT, enhancing understanding of particle motion in these backgrounds.

Contribution

It provides explicit formulas for particle trajectories in a broad class of 2D gravity theories, extending previous work to include multiple models with the Birkhoff theorem.

Findings

Explicit particle trajectories derived for several 2D gravity models

Unified approach applicable to CGHS, JT, and s-wave Einstein gravity

Enhanced understanding of classical particle motion in 2D gravitational backgrounds

Abstract

We provide a method to determine the motion of a classical massive particle in a background geometry of 2-dimensional gravity theories, for which the Birkhoff theorem holds. In particular, we get the particle trajectory in a continuous class of 2-dimensional dilaton gravity theories that includes the Callan-Giddings-Harvey-Strominger (CGHS) model, the Jackiw-Teitelboim (JT) model, and the $d$-dimensional $s$-wave Einstein gravity. The explicit trajectory expressions for these theories are given along with the discussions on the results.