Maarten van de Meent

Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole

We present the first numerical calculation of the (local) metric perturbation produced by a small compact object moving on an eccentric equatorial geodesic around a Kerr black hole, accurate to first order in the mass ratio. The procedure starts by first solving the Teukolsky equation to obtain the Weyl scalar ?4 using semianalytical methods. The metric perturbation is then reconstructed from ?4 in an (outgoing) radiation gauge, adding the appropriate nonradiative contributions arising from the shifts in mass and angular momentum of the spacetime. As a demonstration we calculate the generalized redshift U as a function of the orbital frequencies ?r and ?? to linear order in the mass ratio, a gauge invariant measure of the conservative corrections to the orbit due to self-interactions. In Schwarzschild, the results surpass the existing result in the literature in accuracy, and we find new estimates for some of the unknown 4PN and 5PN terms in the post-Newtonian expansion of U. In Kerr, we provide completely novel values of U for eccentric equatorial orbits. Calculation of the full self-force will appear in a forthcoming paper.

Completion of metric reconstruction for a particle orbiting a Kerr black hole

Vacuum perturbations of the Kerr metric can be reconstructed from the corresponding perturbation in either of the two Weyl scalars ? 0 or ? 4 , using a procedure described by Chrzanowski and others in the 1970s. More recent work, motivated within the context of self-force physics, extends the procedure to metric perturbations sourced by a particle in a bound geodesic orbit. However, the existing procedure leaves undetermined a certain stationary, axially symmetric piece of the metric perturbation. In the vacuum region away from the particle, this “completion” piece corresponds simply to mass and angular-momentum perturbations of the Kerr background, with amplitudes that are, however, a priori unknown. Here, we present and implement a rigorous method for finding the completion piece. The key idea is to impose continuity, off the particle, of certain gauge-invariant fields constructed from the full (completed) perturbation, in order to determine the unknown amplitude parameters of the completion piece. We implement this method in full for bound (eccentric) geodesic orbits in the equatorial plane of the Kerr black hole. Our results provide a rigorous underpinning of recent results by Friedman et al. for circular orbits and extend them to noncircular orbits.

Conditions for sustained orbital resonances in extreme mass ratio inspirals

We investigate the possibility of sustained orbital resonances in extreme mass ratio inspirals. Using a near-identity averaging transformation, we reduce the equations of motion for a particle moving in Kerr spacetime with self-force corrections in the neighbourhood of a resonant geodesic to a one dimensional equation for a particle moving in an effective potential. From this effective equation we obtain the necessary and sufficient conditions that the self-force needs to satisfy to allow inspiralling orbits to be captured in sustained resonance. Along the way we also obtain the full non-linear expression for the jump in the adiabatic constants of motion incurred as an inspiral transiently evolves through a strong resonance to first-order in the mass ratio. Finally, we find that if the resonance is strong enough to allow capture in sustained resonance, only a small fraction (order of the square root of mass-ratio) of all inspirals will indeed be captured. This makes observation of sustained resonances in EMRIs---if they exist---very unlikely for space based observatories like eLisa.

Self-force corrections to the periapsis advance around a spinning black hole

The linear in mass ratio correction to the periapsis advance of equatorial nearly circular orbits around a spinning black hole is calculated for the first time and to a very high precision, providing a key benchmark for different approaches modeling spinning binaries. The high precision of the calculation is leveraged to discriminate between two recent incompatible derivations of the 4 post-Newtonian equations of motion. Finally, the limit of the periapsis advance near the innermost stable orbit (ISCO) allows the determination of the ISCO shift, validating previous calculations using the first law of binary mechanics. Calculation of the ISCO shift is further extended into the near-extremal regime (with spins up to 1-a=10^{-20}), revealing new unexpected phenomenology. In particular, we find that the shift of the ISCO does not have a well-defined extremal limit but instead continues to oscillate.The linear in mass ratio correction to the periapsis advance of equatorial nearly circular orbits around a spinning black hole is calculated for the first time and to a very high precision, providing a key benchmark for different approaches modeling spinning binaries. The high precision of the calculation is leveraged to discriminate between two recent incompatible derivations of the 4 post-Newtonian equations of motion. Finally, the limit of the periapsis advance near the innermost stable orbit (ISCO) allows the determination of the ISCO shift, validating previous calculations using the first law of binary mechanics. Calculation of the ISCO shift is further extended into the near-extremal regime (with spins up to 1-a=10^{-20}), revealing new unexpected phenomenology. In particular, we find that the shift of the ISCO does not have a well-defined extremal limit but instead continues to oscillate.

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, which is 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 ?4, we perform several consistency checks of the method and numerical implementation, including a check of the balance law relating the orbital average of the self-force to the 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.

Renormalized stress-energy tensor of an evaporating spinning black hole

We provide the first calculation of the renormalized stress-energy tensor (RSET) of a quantum field in Kerr spacetime (describing a stationary spinning black hole). More specifically, we employ a recently developed mode-sum regularization method to compute the RSET of a minimally coupled massless scalar field in the Unruh vacuum state, the quantum state corresponding to an evaporating black hole. The computation is done here for the case a=0.7M, using two different variants of the method: t splitting and φ splitting, yielding good agreement between the two (in the domain where both are applicable). We briefly discuss possible implications of the results for computing semiclassical corrections to certain quantities, and also for simulating dynamical evaporation of a spinning black hole.

Geometry of massless cosmic strings

We study the geometry generated by a massless cosmic string. We find that this is given by a Riemann flat spacetime with a conical singularity along the worldsheet of the string. The geometry of such a spacetime is completely fixed by the holonomy of a simple loop wrapping the conical singularity. In the case of a massless cosmic string, this holonomy is a null-rotation/parabolic Lorentz transformation with a parabolic angle given by the linear energy density of the cosmic string. This description explicitly shows that there is no gravitational shockwave accompanying the massless cosmic string as has been suggested in the past. To illustrate the non-singular nature of the surrounding geometry, we construct a metric for the massless cosmic string that is smooth everywhere outside the conical singularity.

Numerical computation of the effective-one-body potential

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 nonspinning compact objects in the extreme mass-ratio limit is given in terms of three potentials: a(v), d¯(v), q(v). By generalizing the first law of mechanics for (nonspinning) black hole binaries to eccentric orbits, [A. Le Tiec, Phys. Rev. D 92, 084021 (2015).] recently obtained new expressions for 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?v?1/6. Our computation thus provides the first-ever strong-field results for q(v). We also obtain d¯(v) in our entire domain to a fractional accuracy of ?10-8. We find that our results are compatible with the known post-Newtonian expansions for d¯(v) and q(v) in the weak field, and agree with previous (less accurate) numerical results for d¯(v) in the strong field.

q

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

using self-force results

\epsilon=m/M