Exact General Relativistic Discs and the Advance of Perihelion

TL;DR

This paper calculates the perihelion advance in various exact general relativistic disc models, providing analytical and numerical results, and compares relativistic precession with Newtonian predictions.

Contribution

It presents new calculations of perihelion precession for several exact relativistic disc solutions, including static and stationary models, with analysis of eccentricity effects.

Findings

Perihelion advance can increase or decrease with orbital eccentricity.

Relativistic precession differs from Newtonian predictions in these disc models.

Analytical and numerical methods are used to evaluate precession in different geometries.

Abstract

The advance of perihelion for geodesic motion on the galactic plane of some exact general relativistic disc solutions is calculated. Approximate analytical and numerical results are presented for the static Chazy-Curzon and the Schwarzschild discs in Weyl coordinates, the Schwarzschid disc in isotropic coordinantes and the stationary Kerr disc in the Weyl-Lewis-Papapetrou metrics. It is found that for these disc models the advance of perihelion may be an increasing or decreasing function of the orbital excentricity. The precession due to Newtonian gravity for these disc models is also calculated.