Second-order gravitational self-force in a highly regular gauge: Covariant and coordinate punctures
arXiv:2309.03778 · doi:10.1103/PhysRevD.109.044021
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.
arXiv comment21 pages, 3 figures. Version to appear in PRD
References in corpus (62)
- Coevolution (Or Not) of Supermassive Black Holes and Host Galaxies
- The Galactic Center Massive Black Hole and Nuclear Star Cluster
- Black holes, gravitational waves and fundamental physics: a roadmap
- The motion of point particles in curved spacetime
- Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals
- Self-force and radiation reaction in general relativity
- Prospects for Fundamental Physics with LISA
- Gravitational self force in extreme mass-ratio inspirals
- New Horizons for Fundamental Physics with LISA
- Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors
- Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
- xTras: a field-theory inspired xAct package for Mathematica
- xPerm: fast index canonicalization for tensor computer algebra
- xPert: Computer algebra for metric perturbation theory
- A Rigorous Derivation of Gravitational Self-force
- Gravitational waveforms for compact binaries from second-order self-force theory
- Second-order gravitational self-force
- Second-order self-force calculation of the gravitational binding energy in compact binaries
- Gravitational self force on a particle in circular orbit around a Schwarzschild black hole
- Evolution of inspiral orbits around a Schwarzschild black hole
- Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency
- Gravitational self-force on generic bound geodesics in Kerr spacetime
- The self-consistent gravitational self-force
- Gravitational-wave energy flux for compact binaries through second order in the mass ratio
- Two-timescale evolution of extreme-mass-ratio inspirals: waveform generation scheme for quasicircular orbits in Schwarzschild spacetime
- Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation
- Second Order Gravitational Self-Force
- Highly eccentric inspirals into a black hole
- Black hole perturbation theory and gravitational self-force
- Nonlinear gravitational self-force: second-order equation of motion
- Regularization of fields for self-force problems in curved spacetime: foundations and a time-domain application
- Geometry and dynamics of a tidally deformed black hole
- Research Update on Extreme-Mass-Ratio Inspirals
- Extreme mass ratio inspirals with spinning secondary: a detailed study of equatorial circular motion
- 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
- Gravitational radiation reaction and second order perturbation theory
- Fast Self-forced Inspirals
- Self-Force Calculations with a Spinning Secondary
- m-Mode Regularization Scheme for the Self Force in Kerr Spacetime
- Hamilton-Jacobi equation for spinning particles near black holes
- Assessing the detectability of the secondary spin in extreme mass-ratio inspirals with fully-relativistic numerical waveforms
- Motion of small objects in curved spacetimes: An introduction to gravitational self-force
- High-order expansions of the Detweiler-Whiting singular field in Schwarzschild spacetime
- Applying the effective-source approach to frequency-domain self-force calculations: Lorenz-gauge gravitational perturbations
- 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
- Dissipation in extreme-mass ratio binaries with a spinning secondary
- Spinning test body orbiting around a Kerr black hole: Eccentric equatorial orbits and their asymptotic gravitational-wave fluxes
- Second-order perturbation theory: the problem of infinite mode coupling
- Second-order gravitational self-force in a highly regular gauge
- Construction of the second-order gravitational perturbations produced by a compact object
- Applying the effective-source approach to frequency-domain self-force calculations
- Transport Equation Approach to Calculations of Hadamard Green functions and non-coincident DeWitt coefficients
- Adiabatic equatorial inspirals of a spinning body into a Kerr black hole
- Quasi-local contribution to the scalar self-force: Non-geodesic Motion
- Self-force: Computational Strategies
- Generating exact solutions to Einstein's equation using linearized approximations
- Slow evolution of the metric perturbation due to a quasicircular inspiral into a Schwarzschild black hole
- The not-so-nonlinear nonlinearity of Einstein's equation
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- 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