Self-force with (3+1) codes: a primer for numerical relativists

Abstract

Prescriptions for numerical self-force calculations have traditionally been designed for frequency-domain or (1+1) time-domain codes which employ a mode decomposition to facilitate in carrying out a delicate regularization scheme. This has prevented self-force analyses from benefiting from the powerful suite of tools developed and used by numerical relativists for simulations of the evolution of comparable-mass black hole binaries. In this work, we revisit a previously-introduced (3+1) method for self-force calculations, and demonstrate its viability by applying it to the test case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. Two (3+1) codes originally developed for numerical relativity applications were independently employed, and in each we were able to compute the two independent components of the self-force and the energy flux correctly to within $<1$. We also demonstrate consistency between $t$-component of the self-force and the scalar energy flux. Our results constitute the first successful calculation of a self-force in a (3+1) framework, and thus open opportunities for the numerical relativity community in self-force analyses and the perturbative modeling of extreme-mass-ratio inspirals.

23 pages, 13 figures

References in corpus (14)

• Intermediate and Extreme Mass-Ratio Inspirals -- Astrophysics, Science Applications and Detection using LISA
• Towards adiabatic waveforms for inspiral into Kerr black holes: I. A new model of the source for the time domain perturbation equation
• Scalar-field perturbations from a particle orbiting a black hole using numerical evolution in 2+1 dimensions
• Scalar self-force on eccentric geodesics in Schwarzschild spacetime: a time-domain computation
• A numerical study of the quasinormal mode excitation of Kerr black holes
• Self force on a scalar charge in Kerr spacetime: circular equatorial orbits
• Self-Force Calculations with Matched Expansions and Quasinormal Mode Sums
• m-Mode Regularization Scheme for the Self Force in Kerr Spacetime
• A new numerical method to construct binary neutron star initial data
• Mode-sum regularization of the scalar self-force: Formulation in terms of a tetrad decomposition of the singular field
• Black hole evolution with the BSSN system by pseudo-spectral methods
• An Efficient Pseudospectral Method for the Computation of the Self-force on a Charged Particle: Circular Geodesics around a Schwarzschild Black Hole
• Accurate time-domain gravitational waveforms for extreme-mass-ratio binaries
• Time domain calculation of the electromagnetic self-force on eccentric geodesics in Schwarzschild spacetime

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• Persistent junk solutions in time-domain modeling of extreme mass ratio binaries
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• New self-force method via elliptic partial differential equations for Kerr inspiral models
• A nonlinear scalar model of extreme mass ratio inspirals in effective field theory I. Self force through third order
• A nonlinear scalar model of extreme mass ratio inspirals in effective field theory II. Scalar perturbations and a master source
• Scalar self-force for eccentric orbits around a Schwarzschild black hole
• Worldtube excision method for intermediate-mass-ratio inspirals: scalar-field model in 3+1 dimensions
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