Relativistic dust disks and the Wilson-Mathews approach
Willy Kley, Gerhard Schaefer (TPI, University of Jena)
TL;DR
This paper compares the full general relativity solutions of a relativistic rotating dust disk with the Wilson-Mathews approximation, finding similar accuracy to the first post-Newtonian method.
Contribution
It provides a comparative analysis of exact and approximate solutions for relativistic dust disks using the Wilson-Mathews approach.
Findings
Wilson-Mathews method has similar accuracy to first post-Newtonian approximation.
Full and approximate solutions show close agreement.
The approach offers a simplified yet accurate method for modeling relativistic disks.
Abstract
Treating problems in full general relativity is highly complex and frequently approximate methods are employed to simplify the solution. We present comparative solutions of a infinitesimally thin relativistic, stationary, rigidly rotating disk obtained using the full equations and the approximate approach suggested by Wilson & Mathews. We find that the Wilson-Mathews method has about the same accuracy as the first post-Newtonian approximation.
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