Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0908.2138

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

Ian Vega·Peter Diener·Wolfgang Tichy·Steven Detweiler
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

gr-qc

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ian Vega, Peter Diener, Wolfgang Tichy, Steven Detweiler. 2009-08-14. Self-force with (3+1) codes: a primer for numerical relativists. https://doi.org/10.1103/physrevd.80.084021

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Complex frequency evolution of direct waves from binary black hole mergers

While no signal originating at a black hole's event horizon can reach future null infinity, information about the horizon and its immediate vicinity can be encoded in asymptotic properties of waves emitted by matter or field perturbations falling toward a growing/forming horizon. Within a response-filtered framework, "direct wave" denotes source-sensitive plunge and remnant-formation information revealed by filtering the black-hole response. Unlike a stationary damped sinusoid with a fixed complex frequency, the direct wave follows the evolving source and has an evolving instantaneous complex frequency tied at late times to the remnant horizon angular velocity $Ω_H$ and surface gravity $κ_H$. Using rational filters, we remove quasinormal modes from numerical-relativity waveforms to study this evolution. Before numerical contamination, trajectories depend on remnant spin: the real frequency evolves toward $2Ω_H$ from above for lower spins ($χ_f\lesssim0.7$) and from below for higher spins ($χ_f\gtrsim0.7$), while the instantaneous decay rate increases, with best-resolved cases approaching the expected value of $3κ_H$. As in particle-plunge results, the horizon-controlled value is approached only at late times, as frame dragging controls near-horizon motion. For $χ_f\sim0.7$ remnants of non-precessing, comparable-mass binaries, the early-time real frequency is close to $2Ω_H$ because the binary orbital frequency transitions smoothly to the remnant horizon frequency. Finite-time deviations therefore carry information about merger/collapse dynamics rather than undermining the horizon connection. Full direct-wave evolution requires numerical-relativity calibration. We further show that approximate pole-zero pairing in the Kerr response motivates a minimal filter set that suppresses quasinormal-mode features while revealing source-trajectory information.

gr-qc↗
arXiv2026

Misinterpreting spin precession as orbital eccentricity in gravitational-wave signals

The increasing scope and breadth of gravitational wave detectors is providing the opportunity to explore new parameters in gravitational-wave astronomy. Eccentricity and spin-precession are two key observables to infer the origin of a gravitational wave (GW) source. The interpretation of GW source parameters can be plagued by degeneracy, such as the well-known degeneracy between mass and spin. As the field has explored new parameters, questions have been raised about possible degeneracies between eccentricity and spin-precession. Although some state-of-the-art models now include these effects individually, models that incorporate spin-precession and eccentricity are only in their infancy. Until models faithfully cover the complete parameter space of compact binary coalescence, our ability to correctly measure the source parameters and infer the formation of the binary is compromised. Here, we present a study of the distinguishability of these two key parameters in heavy binary black hole systems. We study merger-ringdown dominated systems with detector-frame total masses ranging between $200-300M_{\odot}$ and mass ratio ranging between $1-3$. Our work finds that there is indeed a degeneracy between eccentricity and spin-precession; however, it is a highly localized effect. We find that the misidentified eccentricity estimates get worse as the detector-frame total mass increases from $200M_{\odot}$ to $300M_{\odot}$, corresponding to progressively shorter signals in the detector band. Additionally, this misidentification is highly sensitive to the inclination angle of the source system. We provide quantifiable estimates of the potency of this degeneracy in addition to identifying some of the regions of parameter space where this degeneracy exists.

gr-qc↗
arXiv2026

Entropy and stability of an extremally charged Einstein-Born-Infeld thin shell

Spacetimes with a thin shell offer a framework where both the dynamical and the thermodynamical stability of the matter comprising the shell can be consistently studied. In the present work, we consider the dynamical and the thermodynamical stability of a spherical thin shell in Einstein gravity coupled to Born-Infeld electrodynamics. For our construction, we adopt the extremally charged solution of the theory, which gives a closed analytic form for the horizon location that allows for a clear derivation of the corresponding physical quantities of interest. Under this scenario, the dynamical stability conditions under radial perturbations are readily obtained in terms of an effective potential. The equilibrium thermodynamics for such a shell is presented. We find that, despite a non-zero pressure at the shell (unlike the extremally charged Reissner-Nordström counterpart), its entropy is solely characterized as a function of the gravitational radius. We propose a physically suitable \emph{ansatz} for the relevant equations of state in order to obtain a closed expression for the entropy density of the shell. We find that the thermodynamical stability conditions reduce to a single inequality related to exchanges of the charge at the shell, which determines the domain where both dynamical and thermodynamical stable configurations exist.

gr-qc↗