How to use S-metric to periastron precession of binary stars

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Discussion Overview

The discussion revolves around the application of the Schwarzschild metric to the periastron precession of binary stars, specifically addressing the challenges posed by the two-body problem in general relativity. Participants explore the conditions under which the Schwarzschild metric can be adapted for binary systems and seek references or derivations related to this approximation.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes that the Schwarzschild metric can be used to calculate the precession of an orbit, but questions how to apply it when both stars in a binary system have significant mass.
  • Another participant references the two-body problem in general relativity, indicating that there is no closed form solution available.
  • A participant expresses awareness of the lack of an analytical solution and specifically seeks a derivation for the approximation using the total mass M = m1 + m2.
  • Additional references, including a Wikipedia link and a paper from arXiv, are provided to support the discussion.

Areas of Agreement / Disagreement

Participants generally agree on the complexity of the two-body problem and the absence of a closed form solution, but there is no consensus on the specifics of applying the Schwarzschild metric to binary stars or on the derivation of the approximation.

Contextual Notes

The discussion highlights limitations in existing references and derivations related to the application of the Schwarzschild metric to binary star systems, as well as the dependence on the assumption that the total mass can be treated as a single central mass.

Who May Find This Useful

Researchers and students interested in general relativity, binary star systems, and the mathematical challenges of the two-body problem may find this discussion relevant.

Vincentius
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The Schwarzschild metric allows to calculate the precession of an elliptic orbit of a particle around a large central mass, provided the mass of the particle is much smaller than the central mass M. This condition is not met in the case of binary stars m1 and m2 revolving around each other.
There is mention of a possibility of still using the Schwarzschild metric, but then one must take the sum of the masses of the two stars for the central mass, i.e. M=m1+m2.
I can imagine this works, but don't know how. Could anyone supply a reference on this subject.
Thanks!
 
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Yes, I know there is no analytical solution, that's why I asked about the approximation using M=m1+m2. But I cannot find a derivation of this approximate solution. Can anyone help out? Thanks
 
Vincentius said:
Yes, I know there is no analytical solution, that's why I asked about the approximation using M=m1+m2. But I cannot find a derivation of this approximate solution. Can anyone help out? Thanks
This is the only paper on this subject I've got - arXiv:gr-qc/0502062v1 14 Feb 2005.
 

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