Sarp Akcay

Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring

We compute the conservative piece of the gravitational self-force (GSF) acting on a particle of mass m1 as it moves along an (unstable) circular geodesic orbit between the innermost stable orbit and the light ring of a Schwarzschild black hole of mass m2?m1. More precisely, we construct the function huuR,L(x)?h??R,Lu?u? (related to Detweiler’s gauge-invariant “redshift” variable), where h??R,L(?m1) is the regularized metric perturbation in the Lorenz gauge, u? is the four-velocity of m1 in the background Schwarzschild metric of m2, and x?[Gc-3(m1+m2)?]2/3 is an invariant coordinate constructed from the orbital frequency ?. In particular, we explore the behavior of huuR,L just outside the “light ring” at x=1/3 (i.e., r=3Gm2/c2), where the circular orbit becomes null. Using the recently discovered link between huuR,L and the piece a(u), linear in the symmetric mass ratio ??m1m2/(m1+m2)2, of the main radial potential A(u,?)=1-2u+?a(u)+O(?2) of the effective-one-body (EOB) formalism, we compute from our GSF data the EOB function a(u) over the entire domain 0<u<1/3 (thereby extending previous results limited to u?1/5). We find that a(u) diverges like a(u)?0.25(1-3u)-1/2 at the light-ring limit, u?(1/3)-, explain the physical origin of this divergent behavior, and discuss its consequences for the EOB formalism. We construct accurate global analytic fits for a(u), valid on the entire domain 0<u<1/3 (and possibly beyond), and give accurate numerical estimates of the values of a(u) and its first three derivatives at the innermost stable circular orbit u=1/6, as well as the associated O(?) shift in the frequency of that orbit. In previous work we used GSF data on slightly eccentric orbits to compute a certain linear combination of a(u) and its first two derivatives, involving also the O(?) piece of a second EOB radial potential D? (u)=1+?d? (u)+O(?2). Combining these results with our present global analytic representation of a(u), we numerically compute d? (u) on the interval 0<u?1/6

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.

A Fast Frequency-Domain Algorithm for Gravitational Self-Force: I. Circular Orbits in Schwarzschild Spacetime

Fast, reliable orbital evolutions of compact objects around massive black holes will be needed as input for gravitational wave search algorithms in the data stream generated by the planned Laser Interferometer Space Antenna (LISA). Currently, the state of the art is a time-domain code by [Phys. Rev. D{\bf 81}, 084021, (2010)] that computes the gravitational self-force on a point-particle in an eccentric orbit around a Schwarzschild black hole. Currently, time-domain codes take up to a few days to compute just one point in parameter space. In a series of articles, we advocate the use of a frequency-domain approach to the problem of gravitational self-force (GSF) with the ultimate goal of orbital evolution in mind. Here, we compute the GSF for a particle in a circular orbit in Schwarzschild spacetime. We solve the linearized Einstein equations for the metric perturbation in Lorenz gauge. Our frequency-domain code reproduces the time-domain results for the GSF up to

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

\sim 1000

Critical phenomena at the threshold of immediate merger in binary black hole systems: the extreme mass ratio case

times faster for small orbital radii. In forthcoming companion papers, we will generalize our frequency-domain methods to include bound (eccentric) orbits in Schwarzschild and (eventually) Kerr spacetimes for computing the GSF, where we will employ the method of extended homogeneous solutions [Phys. Rev. D {\bf 78}, 084021 (2008)].

Numerical computation of the effective-one-body potential

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 [L. Barack, A. Ori, and N. Sago, Phys. Rev. D 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; (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 3 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 [N. Warburton, S. Akcay, L. Barack, J.?R. Gair, and N. Sago, Phys. Rev. D 85, 061501(R) (2012)]. Here we provide full technical details of our method to complement the above report.

q

In numerical simulations of black hole binaries, Pretorius and Khurana [ Classical Quantum Gravity 24 S83 (2007)] have observed critical behavior at the threshold between scattering and immediate merger. The number of orbits scales as n?-?ln?|p-p*| along any one-parameter family of initial data such that the threshold is at p=p*. Hence, they conjecture that in ultrarelativistic collisions almost all the kinetic energy can be converted into gravitational waves if the impact parameter is fine-tuned to the threshold. As a toy model for the binary, they consider the geodesic motion of a test particle in a Kerr black hole spacetime, where the unstable circular geodesics play the role of critical solutions, and calculate the critical exponent ?. Here, we incorporate radiation reaction into this model using the self-force approximation. The critical solution now evolves adiabatically along a sequence of unstable circular geodesic orbits under the effect of the self-force. We confirm that almost all the initial energy and angular momentum are radiated on the critical solution. Our calculation suggests that, even for infinite initial energy, this happens over a finite number of orbits given by n??0.41/?, where ? is the (small) mass ratio. We derive expressions for the time spent on the critical solution, number of orbits and radiated energy as functions of the initial energy and impact parameter

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 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.

Self-force correction to geodetic spin precession in Kerr spacetime

We present an expression for the gravitational self-force correction to the geodetic spin precession of a spinning compact object with small, but non-negligible mass in a bound, equatorial orbit around a Kerr black hole. We consider only conservative back-reaction effects due to the mass of the compact object (

Horizon-absorbed energy flux in circularized, nonspinning black-hole binaries and its effective-one-body representation

m_1