Gravitational self-force on eccentric equatorial orbits around a Kerr black hole

This paper presents the first calculation of the gravitational self-force on a small compact object on an eccentric equatorial orbit around a Kerr black hole to first order in the mass-ratio. That is the pointwise correction to the object's equations of motion (both conservative and dissipative) due to its own gravitational field treated as a linear perturbation to the background Kerr spacetime generated by the much larger spinning black hole. The calculation builds on recent advances on constructing the local metric and self-force from solutions of the Teukolsky equation, which led to the calculation of the Detweiler-Barack-Sago redshift invariant on eccentric equatorial orbits around a Kerr black hole in a previous paper. After deriving the necessary expression to obtain the self-force from the Weyl scalar $\psi_4$, we perform several consistency checks of the method and numerical implementation, including a check of the balance law relating orbital average of the self-force to average flux of energy and angular momentum out of the system. Particular attention is paid to the pointwise convergence properties of the sum over frequency modes in our method, identifying a systematic inherent loss of precision that any frequency domain calculation of the self-force on eccentric orbits must overcome.Comment: Various typos and correction to match version accepted for publication in PR

Gravitational self-force on generic bound geodesics in Kerr spacetime

In this work we present the first calculation of the gravitational self-force on generic bound geodesics in Kerr spacetime to first order in the mass-ratio. That is, the local correction to equations of motion for a compact object orbiting a larger rotating black hole due to its own impact on the gravitational field. This includes both dissipative and conservative effects. Our method builds on and extends earlier methods for calculating the gravitational self-force on equatorial orbits. In particular we reconstruct the local metric perturbation in the outgoing radiation gauge from the Weyl scalar $\psi_4$, which in turn is obtained by solving the Teukolsky equation using semi-analytical frequency domain methods. The gravitational self-force is subsequently obtained using (spherical) $l$-mode regularization. We test our implementation by comparing the large $l$-behaviour against the analytically known regularization parameters. In addition we validate our results be comparing the long-term average changes to the energy, angular momentum, and Carter constant to changes to these constants of motion inferred from the gravitational wave flux to infinity and down the horizon

Resonantly enhanced kicks from equatorial small mass-ratio inspirals

We calculate the kick generated by an eccentric black hole binary inspiral as it evolves through a resonant orbital configuration where the precession of the system temporarily halts. As a result, the effects of the asymmetric emission of gravitational waves build up coherently over a large number of orbits. Our results are calculate using black hole perturbation theory in the limit where the ratio of the masses of the orbiting objects $\epsilon=m/M$ is small. The resulting kick velocity scales as $\epsilon^{3/2}$, much faster than the $\epsilon^2$ scaling of the kick generated by the final merger. For the most extreme case of a very eccentric ($e\sim 1$) inspiral around a maximally spinning black hole, we find kicks close to $30,000\;\epsilon^{3/2}$~km/s, enough to dislodge a black hole from its host cluster or even galaxy. In reality, such extreme inspirals should be very rare. Nonetheless, the astrophysical impact of kicks in less extreme inspirals could be astrophysically significant.Comment: Updated to match published versio

Numerical computation of the EOB potential q using self-force results

The effective-one-body theory (EOB) describes the conservative dynamics of compact binary systems in terms of an effective Hamiltonian approach. The Hamiltonian for moderately eccentric motion of two non-spinning compact objects in the extreme mass-ratio limit is given in terms of three potentials: $a(v), \bar{d}(v), q(v)$. By generalizing the first law of mechanics for (non-spinning) black hole binaries to eccentric orbits, [\prd{\bf92}, 084021 (2015)] recently obtained new expressions for $\bar{d}(v)$ and $q(v)$ in terms of quantities that can be readily computed using the gravitational self-force approach. Using these expressions we present a new computation of the EOB potential $q(v)$ by combining results from two independent numerical self-force codes. We determine $q(v)$ for inverse binary separations in the range $1/1200 \le v \lesssim 1/6$. Our computation thus provides the first-ever strong-field results for $q(v)$. We also obtain $\bar{d}(v)$ in our entire domain to a fractional accuracy of $\gtrsim 10^{-8}$. We find to our results are compatible with the known post-Newtonian expansions for $\bar{d}(v)$ and $q(v)$ in the weak field, and agree with previous (less accurate) numerical results for $\bar{d}(v)$ in the strong field.Comment: 4 figures, numerical data at the end. Fixed the typos, added the journal referenc

Fast Self-forced Inspirals

We present a new, fast method for computing the inspiral trajectory and gravitational waves from extreme mass-ratio inspirals that can incorporate all known (and future) self-force results. Using near-identity (averaging) transformations we formulate equations of motion that do not explicitly depend upon the orbital phases of the inspiral, making them fast to evaluate, and whose solutions track the evolving constants of motion, orbital phases and waveform phase of a full self-force inspiral to $O(\eta)$, where $\eta$ is the (small) mass ratio. As a concrete example, we implement these equations for inspirals of non-spinning (Schwarzschild) binaries. Our code computes inspiral trajectories in milliseconds which is a speed up of 2-5 orders of magnitude (depending on the mass-ratio) over previous self-force inspiral models which take minutes to hours to evaluate. Computing two-year duration waveforms using our new model we find a mismatch better than $\sim 10^{-4}$ with respect to waveforms computed using the (slower) full self-force models. The speed of our new approach is comparable with kludge models but has the added benefit of easily incorporating self-force results which will, once known, allow the waveform phase to be tracked to sub-radian accuracy over an inspiral.Comment: 33 pages, code available at http://bhptoolkit.org

Piecewise Flat Gravity in 3+1 dimensions

We study a model for gravity in 3+1 dimensions, inspired in general relativity in 2+1 dimensions. In contrast regular general relativity in 3+1 dimensions, the model postulates that space in absence of matter is flat. The requirement that the Einstein equation still holds for the complete spacetime, implies that matter may only appear as conical defects of co-dimension 2, which may be interpreted as straight cosmic strings moving at a constant velocity. The study of collisions of these defects reveals that the dynamics of the model is incomplete. Certain highly energetic collisions of almost parallel defects suggest that no dynamic completion may exist that is fully compatible with the principles on which the model was based. We also study the phase space of the model in the continuum limit. We find that even though does not contain gravitational waves at the fundamental level, they do appear as an emergent feature in the continuum limit.Comment: PhD thesis, Utrecht Universit

Kerr-fully Diving into the Abyss: Analytic Solutions to Plunging Geodesics in Kerr

We present closed-form solutions for plunging geodesics in the extended Kerr spacetime using Boyer-Lindquist coordinates. Our solutions directly solve for the dynamics of generic timelike plunges, we also specialise to the case of test particles plunging from a precessing innermost stable circular orbit (ISSO). We find these solutions in the form of elementary and Jacobi elliptic functions parameterized by Mino time. In particular, we demonstrate that solutions for the ISSO case can be determined almost entirely in terms of elementary functions, depending only on the spin parameter of the black hole and the radius of the ISSO. This extends recent work on the case of equatorial plunges from the innermost stable circular orbit. Furthermore, we introduce a new equation that characterizes the radial inflow from the ISSO to the horizon, taking into account the inclination. For ease of application, our results have been implemented in the KerrGeodesics package in the Black Hole Perturbation Toolkit.Comment: 22 pages, 7 Figure