arXiv subjects

Niels Warburton

Publications and source records attributed to Niels Warburton.

60 records · Page 4Linked to original sources

arXiv2014

Applying the effective-source approach to frequency-domain self-force calculations

The equations of motion of a point particle interacting with its own field are defined in terms of a certain regularized self-field. Two of the leading methods for computing this regularized field are the mode-sum and effective-source approaches. In this work we unite these two distinct regularization schemes by generalizing traditional frequency-domain mode-sum calculations to incorporate effective-source techniques. For a toy scalar-field model we analytically compute an appropriate puncture field from which the regularized residual field can be calculated. To demonstrate the method, we compute the self-force for a scalar particle on a circular orbit in Schwarzschild spacetime. We also demonstrate the relation between the worldtube and window function approaches to localizing the puncture field to the neighborhood of the worldline and show how the method reduces to the well-known mode-sum regularization scheme in a certain limit. This new computational scheme can be applied to cases where traditional mode-sum regularization is inadequate, such as in calculations at second perturbative order.

gr-qc↗

arXiv2014

Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole

For a self-gravitating particle of mass μin orbit around a Kerr black hole of mass M >> μ, we compute the O(μ/M) shift in the frequency of the innermost stable circular equatorial orbit (ISCEO) due to the conservative piece of the gravitational self-force acting on the particle. Our treatment is based on a Hamiltonian formulation of the dynamics in terms of geodesic motion in a certain locally-defined effective smooth spacetime. We recover the same result using the so-called first law of binary black-hole mechanics. We give numerical results for the ISCEO frequency shift as a function of the black hole's spin amplitude, and compare with predictions based on the post-Newtonian approximation and the effective one-body model. Our results provide an accurate strong-field benchmark for spin effects in the general relativistic two-body problem.

gr-qc↗

arXiv2014

Gravitational self-torque and spin precession in compact binaries

We calculate the effect of self-interaction on the "geodetic" spin precession of a compact body in a strong-field orbit around a black hole. Specifically, we consider the spin precession angle $ψ$ per radian of orbital revolution for a particle carrying mass $μ$ and spin $s \ll (G/c) μ^2$ in a circular orbit around a Schwarzschild black hole of mass $M \gg μ$. We compute $ψ$ through $O(μ/M)$ in perturbation theory, i.e, including the correction $δψ$ (obtained numerically) due to the torque exerted by the conservative piece of the gravitational self-field. Comparison with a post-Newtonian (PN) expression for $δψ$, derived here through 3PN order, shows good agreement but also reveals strong-field features which are not captured by the latter approximation. Our results can inform semi-analytical models of the strong-field dynamics in astrophysical binaries, important for ongoing and future gravitational-wave searches.

gr-qc↗

arXiv2013

Evolution of inspiral orbits around a Schwarzschild black hole

We present results from calculations of the orbital evolution in eccentric binaries of nonrotating black holes with extreme mass-ratios. Our inspiral model is based on the method of osculating geodesics, and is the first to incorporate the full gravitational self-force (GSF) effect, including conservative corrections. The GSF information is encapsulated in an analytic interpolation formula based on numerical GSF data for over a thousand sample geodesic orbits. We assess the importance of including conservative GSF corrections in waveform models for gravitational-wave searches.

gr-qc↗

arXiv2013

Frequency-domain algorithm for the Lorenz-gauge gravitational self-force

State-of-the-art computations of the gravitational self-force (GSF) on massive particles in black hole spacetimes involve numerical evolution of the metric perturbation equations in the time-domain, which is computationally very costly. We present here a new strategy, based on a frequency-domain treatment of the perturbation equations, which offers considerable computational saving. The essential ingredients of our method are (i) a Fourier-harmonic decomposition of the Lorenz-gauge metric perturbation equations and a numerical solution of the resulting coupled set of ordinary equations with suitable boundary conditions; (ii) a generalized version of the method of extended homogeneous solutions [Phys. Rev. D {\bf 78}, 084021 (2008)] used to circumvent the Gibbs phenomenon that would otherwise hamper the convergence of the Fourier mode-sum at the particle's location; and (iii) standard mode-sum regularization, which finally yields the physical GSF as a sum over regularized modal contributions. We present a working code that implements this strategy to calculate the Lorenz-gauge GSF along eccentric geodesic orbits around a Schwarzschild black hole. The code is far more efficient than existing time-domain methods; the gain in computation speed (at a given precision) is about an order of magnitude at an eccentricity of 0.2, and up to three orders of magnitude for circular or nearly circular orbits. This increased efficiency was crucial in enabling the recently reported calculation of the long-term orbital evolution of an extreme mass ratio inspiral [Phys. Rev. D {\bf 85}, 061501(R) (2012)]. Here we provide full technical details of our method to complement the above report.

gr-qc↗

arXiv2013

Isofrequency pairing of geodesic orbits in Kerr geometry

Bound geodesic orbits around a Kerr black hole can be parametrized by three constants of the motion: the (specific) orbital energy, angular momentum and Carter constant. Generically, each orbit also has associated with it three frequencies, related to the radial, longitudinal and (mean) azimuthal motions. Here we note the curious fact that these two ways of characterizing bound geodesics are not in a one-to-one correspondence. While the former uniquely specifies an orbit up to initial conditions, the latter does not: there is a (strong-field) region of the parameter space in which pairs of physically distinct orbits can have the same three frequencies. In each such isofrequency pair the two orbits exhibit the same rate of periastron precession and the same rate of Lense-Thirring precession of the orbital plane, and (in a certain sense) they remain "synchronized" in phase.

gr-qc↗