Second-order gravitational self-force in a highly regular gauge: Covariant and coordinate punctures

Abstract

Gravitational self-force theory is the primary way of modelling extreme-mass-ratio inspirals (EMRIs). One difficulty that appears in second-order self-force calculations is the strong divergence at the worldline of the small object, which causes both numerical and analytical issues. Previous work [Phys. Rev. D 95, 104056 (2017); ibid. 103, 124016 (2021)] demonstrated that this could be alleviated within a class of highly regular gauges and presented the metric perturbations in these gauges in a local coordinate form. We build on this previous work by deriving expressions for the highly regular gauge metric perturbations in both fully covariant form and as a generic coordinate expansion. With the metric perturbations in covariant or generic coordinate form, they can easily be expressed in any convenient coordinate system. These results can then be used as input into a puncture scheme in order to solve the field equations describing an EMRI.

21 pages, 3 figures. Version to appear in PRD

References in corpus (17)

• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
• xPerm: fast index canonicalization for tensor computer algebra
• xPert: Computer algebra for metric perturbation theory
• Gravitational-wave energy flux for compact binaries through second order in the mass ratio
• Research Update on Extreme-Mass-Ratio Inspirals
• A practical, covariant puncture for second-order self-force calculations
• Scalar-field perturbations from a particle orbiting a black hole using numerical evolution in 2+1 dimensions
• Nonlinear gravitational self-force. I. Field outside a small body
• Evolution of small-mass-ratio binaries with a spinning secondary
• Self-Force Calculations with a Spinning Secondary
• m-Mode Regularization Scheme for the Self Force in Kerr Spacetime
• Mode-sum regularization of the scalar self-force: Formulation in terms of a tetrad decomposition of the singular field
• Extreme mass ratio inspirals on the equatorial plane in the adiabatic order
• Second-order perturbation theory: the problem of infinite mode coupling
• Construction of the second-order gravitational perturbations produced by a compact object
• Adiabatic equatorial inspirals of a spinning body into a Kerr black hole
• The not-so-nonlinear nonlinearity of Einstein's equation

Cited by in corpus (8)

• Probing fundamental physics with Extreme Mass Ratio Inspirals: a full Bayesian inference for scalar charge
• Implementation of a GHZ-Teukolsky puncture scheme for gravitational self-force calculations
• Multi-domain spectral method for self-force calculations
• Resonant excitation of eccentricity in spherical extreme-mass-ratio inspirals
• Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary
• Toward Second-Order Self-Force for Eccentric Extreme-Mass Ratio Inspirals in Schwarzschild Spacetime
• Analytical model of precessing binaries using post-Newtonian theory in the extreme mass-ratio limit I: General Formalism
• Generic effective sources for first-order in mass-ratio gravitational self-force calculations in Schwarzschild spacetime