Exact Solution for Relativistic Two-Body Motion in Dilaton Gravity

TL;DR

This paper provides an exact analytical solution for the relativistic motion of two point masses in (1+1)-dimensional dilaton gravity, fully describing their dynamics and spacetime geometry.

Contribution

It introduces the first exact solution for two-body relativistic motion in dilaton gravity, including the Hamiltonian to all orders in coupling.

Findings

Exact Hamiltonian derived for two-body system

Static gravitational potential identified

Solution applicable in Newtonian limit

Abstract

We present an exact solution to the problem of the relativistic motion of 2 point masses in $(1+1)$ dimensional dilaton gravity. The motion of the bodies is governed entirely by their mutual gravitational influence, and the spacetime metric is likewise fully determined by their stress-energy. A Newtonian limit exists, and there is a static gravitational potential. Our solution gives the exact Hamiltonian to infinite order in the gravitational coupling constant.