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Effective field theory (EFT) allows studying deviations from general relativity in black hole mergers. New modified harmonic gauges ensure well-posed initial value formulations for numerical simulations of these mergers.

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Area of Science:

  • Theoretical physics
  • Gravitational wave astrophysics
  • Numerical relativity

Background:

  • Effective field theory (EFT) offers a framework to model strong-field deviations from general relativity.
  • Such deviations may be detectable in gravitational waves from black hole mergers.
  • Numerical simulations of these mergers require equations with a well-posed initial value formulation.

Purpose of the Study:

  • To investigate gravity coupled to a scalar field with leading effective field theory corrections.
  • To develop a formulation suitable for numerical simulations of black hole mergers in modified gravity theories.

Main Methods:

  • Studied gravity coupled to a scalar field, including four-derivative EFT corrections.
  • Introduced a new class of modified harmonic gauges.
  • Derived gauge-fixed equations of motion.

Main Results:

  • The proposed modified harmonic gauges and equations of motion are strongly hyperbolic at weak coupling.
  • This hyperbolic nature ensures a well-posed initial value formulation for numerical simulations.
  • Enables the study of strong-field deviations in black hole merger gravitational waves.

Conclusions:

  • The developed formulation is crucial for performing reliable numerical simulations of black hole mergers in effective field theories.
  • This work paves the way for exploring observable gravitational wave signatures of modified gravity.