arXiv subjects

Thomas Osburn

Publications and source records attributed to Thomas Osburn.

11 recordsLinked to original sources

arXiv2026

Schwarzschild perturbations in Lorenz gauge via elliptic differential equations

Accurate predictions of gravitational wave signals from asymmetric compact binaries are accessible through black hole perturbation theory and self-force calculations. Faithful waveform models will require contributions from first- and second-order terms in the small mass-ratio expansion. The problem of second-order Kerr perturbations is exacerbated by non-separability of the metric perturbation equations and non-linear mode coupling, which motivates this $m$-mode approach. This work moves towards the eventual goal of second-order Kerr perturbations by calculating first-order Schwarzschild metric perturbations via $m$-modes in the frequency domain for the first time. We solve the Lorenz gauge field equations as a system of coupled elliptic partial differential equations that govern each $m$-mode. Our Mathematica code implements a second-order finite difference representation of the field equations, which we solve as a sparse linear algebra problem. Regularization near the small body is achieved through the effective source method, and our presentation introduces a new puncture expansion of the singular field for a point mass in Kerr spacetime. Issues related to problematic near-horizon behavior are explored and then mitigated by applying sophisticated near-horizon boundary conditions. Our results illustrate the features of each component and $m$-mode of the metric perturbation, and we are able to calculate gravitational wave energy fluxes with sufficient accuracy to enable future second-order self-force calculations.

gr-qc↗

arXiv2026

Self-force calculations with numerical relativity methods

To model gravitational waveforms from extreme mass-ratio inspirals (EMRIs) for the upcoming LISA space mission, gravitational self-force calculations are needed to second order in perturbation theory. However, to date these calculations have only been attempted for the simplest case of circular orbits in Schwarzschild spacetime. In this work, we present a new computational method aimed at performing generic second-order self-force calculations in Kerr spacetime using methods from the adjacent field of numerical relativity. We perform an $m$-mode separation of variables, add null ("$vtu$") slicing in horizon-penetrating coordinates, and solve the resulting elliptic PDEs using high-order discontinuous Galerkin discretization, adaptive mesh-refinement, and an iterative Krylov-type linear solver with parallelizable multigrid-Schwarz preconditioning. We find that our method achieves exponential convergence for the self-force on a scalar point charge in Kerr spacetime up to spins of $a=0.998$ (Thorne limit) on circular equatorial orbits as close as the ISCO (prograde and retrograde), despite the non-smooth puncture on the grid. We solve for 20 $m$-modes in parallel in a few seconds and retain the flexibility to extend the method to gravitational self-force and more generic orbits in the future. The code to perform these calculations is publicly available in the open-source numerical relativity code SpECTRE.

gr-qc↗

arXiv2022

New self-force method via elliptic partial differential equations for Kerr inspiral models

We present a new method designed to avoid numerical challenges that have impeded calculation of the Lorenz gauge self-force acting on a compact object inspiraling into a Kerr black hole. This type of calculation is valuable in creating waveform templates for extreme mass-ratio inspirals, which are an important source of gravitational waves for the upcoming Laser Interferometer Space Antenna mission. Prior hyperbolic partial differential equation (PDE) formulations encountered numerical instabilities involving unchecked growth in time; our new method is based on elliptic PDEs, which do not exhibit instabilities of that kind. For proof of concept, we calculate the self-force acting on a scalar charge in a circular orbit around a Kerr black hole. We anticipate this method will subsequently facilitate calculation of first-order Lorenz gauge Kerr metric perturbations and self-force, which could serve as a foundation for second-order Kerr self-force investigations.

gr-qc↗

arXiv2021

Highly eccentric EMRI waveforms via fast self-forced inspirals

We present new developments and comparisons of competing inspiral and waveform models for highly eccentric non-spinning extreme and intermediate mass-ratio inspirals (EMRIs and IMRIs). Starting from our high eccentricity self-force library, we apply the near-identity transform (NIT) technique to rapidly compute highly eccentric self-forced inspirals for the first time. Upon evaluating our approximate NIT results via comparison with full self-force inspirals, we couple our accurate and streamlined inspiral data to potential waveform generation schemes. We find that, although high eccentricity strains the NIT method, NIT inspirals are consistent with full self-force inspirals for EMRIs. However, our NIT implementation (at 1st post-adiabatic order) is not able to achieve LISA-motivated accuracy goals for highly eccentric IMRIs. Our most sophisticated waveforms are devised through a new technique that efficiently connects NIT orbital parameters to Teukolsky amplitudes and phases. We compare these sophisticated Teukolsky waveforms to those with synthesized (summing over harmonics) amplitudes based on a kludge. We find that, assuming identical worldlines (so that dephasing is negligible), kludge waveforms compare favorably to Teukolsky waveforms for non-spinning bodies.

gr-qc↗

arXiv2020

Reissner-Nordström perturbation framework with gravitational wave applications

We present a new convenient framework for modeling Reissner-Nordström black hole perturbations from charged distributions of matter. Using this framework, we quantify how gravitational wave observations of compact binary systems would be affected if one or both components were charged. Our approach streamlines the (linearized) Einstein-Maxwell equations through convenient master functions that we designed to ameliorate certain disadvantages of prior strategies. By solving our improved master equations with a point source, we are able to quantify the rate of orbital energy dissipation via electromagnetic and gravitational radiation. Through adiabatic and quasicircular approximations, we apply our dissipative calculations to determine trajectories for intermediate and extreme mass-ratio inspirals. By comparing trajectories and waveforms with varied charges to those with neutral components, we explore the potential effect of electric charge on gravitational wave signals. We observe that the case of opposite charge-to-mass ratios has the most dramatic impact. Our findings are largely interpreted through the lens of the upcoming LISA mission.

gr-qc↗

arXiv2019

Repeated faint quasinormal bursts in extreme-mass-ratio inspiral waveforms: Evidence from frequency-domain scalar self-force calculations on generic Kerr orbits

We report development of a code to calculate the scalar self-force on a scalar-charged particle moving on generic bound orbits in the Kerr spacetime. The scalar self-force model allows rapid development of computational techniques relevant to generic gravitational extreme-mass-ratio inspirals (EMRIs). Our frequency-domain calculations are made with arbitrary numerical precision code written in \textsc{Mathematica}. We extend spectral source integration techniques to the Kerr spacetime, increasing computational efficiency. We model orbits with nearly arbitrary inclinations $0\leqι<π/2$ and eccentricities up to $e \lesssim 0.8$. This effort extends earlier work by Warburton and Barack where motion was restricted to the equatorial plane or to inclined spherical orbits. Consistent with a recent discovery by Thornburg and Wardell \cite{ThorWard17} in time-domain calculations, we observe self-force oscillations during the radially-outbound portion of highly eccentric orbits around a rapidly rotating black hole. As noted previously, these oscillations reflect coupling into the self-force by quasinormal modes excited during pericenter passage. Our results confirm the effect with a frequency-domain code. \emph{More importantly, we find that quasinormal bursts (QNBs) appear directly in the waveform following each periastron passage.} These faint bursts are shown to be a superposition of the least-damped overtone (i.e., fundamental) of at least four ($l=m \le 4$) quasinormal modes. Our results suggest that QNBs should appear in gravitational waveforms, and thus provide a gauge-invariant signal. Potentially observable in high signal-to-noise ratio EMRIs, QNBs would provide high-frequency components to the parameter estimation problem that would complement low-frequency elements of the waveform.

gr-qc↗

arXiv2018

Inspirals into a charged black hole

We model the quasicircular inspiral of a compact object into a more massive charged black hole. Extreme and intermediate mass-ratio inspirals are considered through a small mass-ratio approximation. Reissner-Nordstr$\ddot{\text{o}}$m spacetime is used to describe the charged black hole. The effect of radiation reaction on the smaller body is quantified through calculation of electromagnetic and gravitational energy fluxes via solution of Einstein's and Maxwell's equations. Inspiral trajectories are determined by matching the orbital energy decay rate to the rate of radiative energy dissipation. We observe that inspirals into a charged black hole evolve more rapidly than comparable inspirals into a neutral black hole. Through analysis of a variety of inspiral configurations, we conclude that electric charge is an important effect concerning gravitational wave observations when the charge exceeds the threshold $|Q|/M \gtrsim 0.071 \sqrtε$, where $ε$ is the mass ratio.

gr-qc↗

arXiv2017

Evolution of small-mass-ratio binaries with a spinning secondary

We calculate the evolution and gravitational-wave emission of a spinning compact object inspiraling into a substantially more massive (non-rotating) black hole. We extend our previous model for a non-spinning binary [Phys. Rev. D 93, 064024] to include the Mathisson-Papapetrou-Dixon spin-curvature force. For spin-aligned binaries we calculate the dephasing of the inspiral and associated waveforms relative to models that do not include spin-curvature effects. We find this dephasing can be either positive or negative depending on the initial separation of the binary. For binaries in which the spin and orbital angular momentum are not parallel, the orbital plane precesses and we use a more general osculating element prescription to compute inspirals.

gr-qc↗

arXiv2016

Highly eccentric inspirals into a black hole

We model the inspiral of a compact stellar-mass object into a massive nonrotating black hole including all dissipative and conservative first-order-in-the-mass-ratio effects on the orbital motion. The techniques we develop allow inspirals with initial eccentricities as high as $e\sim0.8$ and initial separations as large as $p\sim 50$ to be evolved through many thousands of orbits up to the onset of the plunge into the black hole. The inspiral is computed using an osculating elements scheme driven by a hybridized self-force model, which combines Lorenz-gauge self-force results with highly accurate flux data from a Regge-Wheeler-Zerilli code. The high accuracy of our hybrid self-force model allows the orbital phase of the inspirals to be tracked to within $\sim0.1$ radians or better. The difference between self-force models and inspirals computed in the radiative approximation is quantified.

gr-qc↗

arXiv2015

Fast spectral source integration in black hole perturbation calculations

This paper presents a new technique for achieving spectral accuracy and fast computational performance in a class of black hole perturbation and gravitational self-force calculations involving extreme mass ratios and generic orbits. Called \emph{spectral source integration} (SSI), this method should see widespread future use in problems that entail (i) point-particle description of the small compact object, (ii) frequency domain decomposition, and (iii) use of the background eccentric geodesic motion. Frequency domain approaches are widely used in both perturbation theory flux-balance calculations and in local gravitational self-force calculations. Recent self-force calculations in Lorenz gauge, using the frequency domain and method of extended homogeneous solutions, have been able to accurately reach eccentricities as high as $e \simeq 0.7$. We show here SSI successfully applied to Lorenz gauge. In a double precision Lorenz gauge code, SSI enhances the accuracy of results and makes a factor of three improvement in the overall speed. The primary initial application of SSI--for us its \emph{raison d'être}--is in an arbitrary precision \emph{Mathematica} code that computes perturbations of eccentric orbits in the Regge-Wheeler gauge to extraordinarily high accuracy (e.g., 200 decimal places). These high accuracy eccentric orbit calculations would not be possible without the exponential convergence of SSI. We believe the method will extend to work for inspirals on Kerr, and will be the subject of a later publication. SSI borrows concepts from discrete-time signal processing and is used to calculate the mode normalization coefficients in perturbation theory via sums over modest numbers of points around an orbit. A variant of the idea is used to obtain spectral accuracy in solution of the geodesic orbital motion.

gr-qc↗

arXiv2014

Lorenz gauge gravitational self-force calculations of eccentric binaries using a frequency domain procedure

We present an algorithm for calculating the metric perturbations and gravitational self-force for extreme-mass-ratio inspirals (EMRIs) with eccentric orbits. The massive black hole is taken to be Schwarzschild and metric perturbations are computed in Lorenz gauge. The perturbation equations are solved as coupled systems of ordinary differential equations in the frequency domain. Accurate local behavior of the metric is attained through use of the method of extended homogeneous solutions and mode-sum regularization is used to find the self-force. We focus on calculating the self-force with sufficient accuracy to ensure its error contributions to the phase in a long term orbital evolution will be $δΦ\lesssim 10^{-2}$ radians. This requires the orbit-averaged force to have fractional errors $\lesssim 10^{-8}$ and the oscillatory part of the self-force to have errors $\lesssim 10^{-3}$ (a level frequently easily exceeded). Our code meets this error requirement in the oscillatory part, extending the reach to EMRIs with eccentricities of $e \lesssim 0.8$, if augmented by use of fluxes for the orbit-averaged force, or to eccentricities of $e \lesssim 0.5$ when used as a stand-alone code. Further, we demonstrate accurate calculations up to orbital separations of $a \simeq 100 M$, beyond that required for EMRI models and useful for comparison with post-Newtonian theory. Our principal developments include (1) use of fully constrained field equations, (2) discovery of analytic solutions for even-parity static modes, (3) finding a pre-conditioning technique for outer homogeneous solutions, (4) adaptive use of quad-precision and (5) jump conditions to handle near-static modes, and (6) a hybrid scheme for high eccentricities.

gr-qc↗