eFTC-251001

Settling the Misner-Yilmaz Controversy in Einstein Real Gravity
6 October 2025

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Abstract

We provide an in-depth analysis of the so-called Misner-Yilmaz controversy regarding the hydrostatic equilibrium of a perfect pascalian fluid in Einstein and Yilmaz General Relativity. While we agree with Misner that the Einstein theory wins the debate, we severely criticize the arguments presented by both Misner and Yilmaz, which turn out to be wrong in many respects. First of all no pascalian fluid solution exists whether in Einstein or Yilmaz General Relativity in cartesian coordinates. Second, the use of the harmonic coordinate condition (the Newton gauge) for an interior problem is wrong. We therefore recalculate the hydrostatic equilibrium within the Einstein Real Gravity formalism, in spherical coordinates and beyond the Newton gauge. We show that it reproduces known results by Landau and Lifchitz for a pascalian fluid obtained in the context of the Einstein Ricci curvature field equations for a time-dependent central symmetric metric. We finally derive the corrected Tolman-Oppenheimer-Volkoff formula for star equilibrium.

Copyright © 2025 Yvan Leblanc. All rights reserved

PACS: 4.60.+n, 11.17.+y, 97.60.Lf

Cite as: Leblanc, Y., "Settling the Misner-Yilmaz Controversy in Einstein Real Gravity", Report no. eFTC-251001 (2025). http://www.efieldtheory.com/abs/?eFTC-251001; doi:10.13140/RG.2.2.19911.97441.