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The Post-Newtonian Approximation for Relativistic Compact Binaries.

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This study details the post-Newtonian approximation in general relativity, deriving precise equations of motion for compact binaries using a novel surface integral approach. The findings offer an unambiguous, Lorentz-invariant description crucial for gravitational wave research.

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Area of Science:

  • General Relativity
  • Astrophysics
  • Theoretical Physics

Background:

  • The post-Newtonian (PN) approximation is essential for describing gravitational systems in the weak-field, slow-motion limit.
  • Accurate equations of motion for compact binaries are crucial for modeling gravitational wave sources.

Purpose of the Study:

  • To present a method for deriving post-Newtonian equations of motion for relativistic compact binaries.
  • To apply this method to derive third post-Newtonian (3PN) equations of motion.
  • To ensure the derived equations respect Lorentz invariance and possess a conserved energy.

Main Methods:

  • Foundation based on the Newtonian limit of general relativity.
  • Surface integral approach for deriving equations of motion.
  • Strong field point particle limit considerations.

Main Results:

  • Derivation of post-Newtonian equations of motion for relativistic compact binaries.
  • Successful application to obtain third post-Newtonian (3PN) equations.
  • The derived 3PN equations are Lorentz-invariant in the post-Newtonian perturbative sense.
  • The 3PN equations admit a conserved energy and are free from ambiguity.

Conclusions:

  • The surface integral approach provides a robust method for deriving PN equations of motion.
  • The derived 3PN equations offer an unambiguous and physically consistent description of compact binary dynamics.
  • This work contributes to more accurate gravitational wave data analysis and theoretical understanding.