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Weyl Double Copy for Gravitational Waves.

Hadi Godazgar1, Mahdi Godazgar2, Ricardo Monteiro3

  • 1Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Mühlenberg 1, D-14476 Potsdam, Germany.

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|March 30, 2021
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Summary
This summary is machine-generated.

The Weyl double copy relation holds for radiative vacuum Einstein equations. Degenerate Maxwell fields on curved spacetime indicate type N vacuum solutions, enabling a double copy interpretation for nontwisting radiative fields.

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Area of Science:

  • General Relativity
  • Theoretical Physics
  • Gravitational Waves

Background:

  • The Weyl double copy relates gravitational and electromagnetic fields.
  • Radiative solutions of Einstein's equations describe gravitational radiation.
  • Type N vacuum solutions are crucial for understanding isolated gravitational systems.

Purpose of the Study:

  • To investigate the validity of the Weyl double copy for radiative vacuum Einstein equations.
  • To establish a connection between degenerate Maxwell fields and type N vacuum solutions.
  • To explore the double copy interpretation of nontwisting radiative solutions.

Main Methods:

  • Analyzing type N vacuum solutions of Einstein's equations.
  • Investigating the properties of degenerate Maxwell fields.
  • Establishing a scalar field satisfying wave equations on curved and Minkowski spacetimes.

Main Results:

  • All type N vacuum solutions admit a degenerate Maxwell field whose square equals the Weyl tensor.
  • The existence of a degenerate Maxwell field on a curved background implies it is type N.
  • Nontwisting radiative solutions exhibit a direct double copy interpretation via Maxwell fields and scalars satisfying wave equations.

Conclusions:

  • The Weyl double copy relation is established for radiative vacuum Einstein equations.
  • Degenerate Maxwell fields serve as a criterion for type N vacuum spacetimes.
  • Nontwisting radiative solutions possess a clear double copy structure, linking gravity and electromagnetism.