Toward Second-Order Self-Force for Eccentric Extreme-Mass Ratio Inspirals in Schwarzschild Spacetime
arXiv:2504.09640 · doi:10.1103/42fh-sw5h
Abstract
An Extreme Mass Ratio Inspiral (EMRI), which corresponds to a small compact object inspirals around a massive black hole in the center of a galaxy, is one of the most important sources for future space-borne gravitational-wave (GW) detectors such as TianQin and LISA. By analyzing the emitted GW signals, we can probe the theory of gravity and the nature of black holes in the strong field region. To achieve these objectives, the second-order self-force effect should be considered in the waveform modeling. Up to now, the waveform of EMRIs including the second-order self-force effect is only achieved for the circular orbit on Schwarzschild background. In this work, we generalized the calculation of the second-order self-force to the eccentric orbits on Schwarzschild spacetime. We calculated the puncture field, and give the form of two-timescale expansion for the field equations. The corresponding numerical calculation and programming can be performed based on these results.
18 pages, 3 figures, 1 table, matches the published version
References in corpus (55)
- TianQin: a space-borne gravitational wave detector
- The motion of point particles in curved spacetime
- Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals
- Gravitational Radiation Reaction to a Particle Motion
- An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime
- Self-force and radiation reaction in general relativity
- Prospects for Fundamental Physics with LISA
- The TianQin project: current progress on science and technology
- Self-force via a Green's function decomposition
- Cosmology with the Laser Interferometer Space Antenna
- New Horizons for Fundamental Physics with LISA
- Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
- Gravitational Waves from a Compact Star in a Circular, Inspiral Orbit, in the Equatorial Plane of a Massive, Spinning Black Hole, as Observed by LISA
- xPerm: fast index canonicalization for tensor computer algebra
- xPert: Computer algebra for metric perturbation theory
- Gravitational waveforms for compact binaries from second-order self-force theory
- Second-order gravitational self-force
- Gravitational self force on a particle in circular orbit around a Schwarzschild black hole
- Osculating orbits in Schwarzschild spacetime, with an application to extreme mass-ratio inspirals
- 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
- Gravitational self force and gauge transformations
- Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation
- Second Order Gravitational Self-Force
- Science with the TianQin observatory: Preliminary result on extreme-mass-ratio inspirals
- 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
- 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
- Gravitational radiation reaction and second order perturbation theory
- Fast Self-forced Inspirals
- Self-Force Calculations with a Spinning Secondary
- Science with the TianQin Observatory: Preliminary Results on Testing the No-hair Theorem with EMRI
- 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
- The role of the supermassive black hole spin in the estimation of the EMRI event rate
- Possible Causes of False General Relativity Violations in Gravitational Wave Observations
- Waveform accuracy and systematic uncertainties in current gravitational wave observations
- Gravitational Wave Astronomy With TianQin
- Applying the effective-source approach to frequency-domain self-force calculations: Lorenz-gauge gravitational perturbations
- Assessing the impact of transient orbital resonances
- Mode-sum regularization of the scalar self-force: Formulation in terms of a tetrad decomposition of the singular field
- Second-order gravitational self-force in a highly regular gauge
- Analytic Kludge Waveforms for Extreme Mass Ratio Inspirals of Charged Object around Kerr-Newman Black Hole
- Applying the effective-source approach to frequency-domain self-force calculations
- Systematic Biases in Estimating the Properties of Black Holes Due to Inaccurate Gravitational-Wave Models
- Generic effective source for scalar self-force calculations
- Systematic bias from waveform modeling for binary black hole populations in next-generation gravitational wave detectors
- Fast inspirals and the treatment of orbital resonances
- Applying the effective-source approach to frequency-domain self-force calculations for eccentric orbits
- Constraining the EdGB Theory with Extreme Mass-Ratio Inspirals
- Gravitational Waves on Kerr Black Holes I: Reconstruction of Linearized Metric Perturbations
- Second-order gravitational self-force in a highly regular gauge: Covariant and coordinate punctures
- Secondary spins of extreme mass ratio inspirals: A probe to the formation channels