Exact Relativistic Two-Body Motion in Lineal Gravity

TL;DR

This paper provides an exact solution for the relativistic two-body problem in (1+1) dimensional lineal gravity, including explicit expressions for proper separation and an exact Hamiltonian to all orders.

Contribution

It introduces the first exact relativistic solution for two-body motion in lineal gravity, with explicit formulas and an all-orders Hamiltonian.

Findings

Exact solution for two-body relativistic motion in lineal gravity.

Explicit expression for proper separation in equal mass case.

Hamiltonian derived to infinite order in gravitational coupling.

Abstract

We consider the N-body problem in (1+1) dimensional lineal gravity. For 2 point masses (N=2) we obtain an exact solution for the relativistic motion. In the equal mass case we obtain an explicit expression for their proper separation as a function of their mutual proper time. Our solution gives the exact Hamiltonian to infinite order in the gravitational coupling constant.