Self-force theory is the leading method of modeling extreme-mass-ratio inspirals (EMRIs), key sources for the gravitational-wave detector LISA. It is well known that for an accurate EMRI model, ...second-order self-force effects are critical, but calculations of these effects have been beset by obstacles. In this Letter we present the first implementation of a complete scheme for second-order self-force computations, specialized to the case of quasicircular orbits about a Schwarzschild black hole. As a demonstration, we calculate the gravitational binding energy of these binaries.
Within the framework of self-force theory, we compute the gravitational-wave energy flux through second order in the mass ratio for compact binaries in quasicircular orbits. Our results are ...consistent with post-Newtonian calculations in the weak field, and they agree remarkably well with numerical-relativity simulations of comparable-mass binaries in the strong field. We also find good agreement for binaries with a spinning secondary or a slowly spinning primary. Our results are key for accurately modeling extreme-mass-ratio inspirals and will be useful in modeling intermediate-mass-ratio systems.
If a small “particle” of mass μM (with μ≪1) orbits a black hole of mass M, the leading-order radiation-reaction effect is an O(μ2) “self-force” acting on the particle, with a corresponding O(μ) ...“self-acceleration” of the particle away from a geodesic. Such “extreme-mass-ratio inspiral” systems are likely to be important gravitational-wave sources for future space-based gravitational-wave detectors. Here we consider the “toy model” problem of computing the self-force for a scalar-field particle on a bound eccentric orbit in Kerr spacetime. We use the Barack-Golbourn-Vega-Detweiler effective-source regularization with a 4th-order puncture field, followed by an eimϕ (“m-mode”) Fourier decomposition and a separate time-domain numerical evolution in 2+1 dimensions for each m. We introduce a finite worldtube that surrounds the particle worldline and define our evolution equations in a piecewise manner so that the effective source is only used within the worldtube. Viewed as a spatial region, the worldtube moves to follow the particle’s orbital motion. We use slices of constant Boyer-Lindquist time in the region of the particle’s motion, deformed to be asymptotically hyperboloidal and compactified near the horizon and J+. Our numerical evolution uses Berger-Oliger mesh refinement with 4th-order finite differencing in space and time. Our computational scheme allows computation for highly eccentric orbits and should be generalizable to orbital evolution in the future. Our present implementation is restricted to equatorial geodesic orbits, but this restriction is not fundamental. We present numerical results for a number of test cases with orbital eccentricities as high as 0.98. In some cases we find large oscillations (“wiggles”) in the self-force on the outgoing leg of the orbit shortly after periastron passage; these appear to be caused by the passage of the orbit through the strong-field region close to the background Kerr black hole.
Second-order self-force computations, which will be essential in modeling extreme-mass-ratio inspirals, involve two major new difficulties that were not present at first order. One is the problem of ...large scales, discussed in Pound Phys. Rev. D 92, 104047 (2015). Here we discuss the second difficulty, which occurs instead on small scales: if we expand the field equations in spherical harmonics, then because the first-order field contains a singularity, we require an arbitrarily large number of first-order modes to accurately compute even a single second-order mode. This is a generic feature of nonlinear field equations containing singularities, allowing us to study it in the simple context of a scalar toy model in flat space. Using that model, we illustrate the problem and demonstrate a robust strategy for overcoming it.
We present an analytic computation of Detweiler's redshift invariant for a point mass in a circular orbit around a Kerr black hole, giving results up to 8.5 post-Newtonian order while making no ...assumptions on the magnitude of the spin of the black hole. Our calculation is based on the functional series method of Mano, Suzuki and Takasugi, and employs a rigorous mode-sum regularization prescription based on the Detweiler-Whiting singular-regular decomposition. The approximations used in our approach are minimal; we use the standard self-force expansion to linear order in the mass ratio, and the standard post-Newtonian expansion in the separation of the binary. A key advantage of this approach is that it produces expressions that include contributions at all orders in the spin of the Kerr black hole. While this work applies the method to the specific case of Detweiler's redshift invariant, it can be readily extended to other gauge-invariant quantities and to higher post-Newtonian orders.
The motion of a charged particle is influenced by the self-force arising from the particle's interaction with its own field. In a curved spacetime, this self-force depends on the entire past history ...of the particle and is difficult to evaluate. As a result, all existing self-force evaluations in curved spacetime are for particles moving along a fixed trajectory. Here, for the first time, we overcome this long-standing limitation and present fully self-consistent orbits and waveforms of a scalar charged particle around a Schwarzschild black hole.
In this work we present an analytical gravitational self-force calculation of the spin-orbit precession along an eccentric orbit around a Schwarzschild black hole, following closely the recent ...prescription of Akcay, Dempsey, and Dolan, giving results to six post-Newtonian orders expanded in small eccentricity through e2. We then transcribe this quantity within the effective-one-body (EOB) formalism, thereby determining several new, linear-in-mass-ratio contributions in the post-Newtonian expansion of the spin-orbit couplings entering the EOB Hamiltonian. Namely, we determine the second gyrogravitomagnetic ratio gS*(r,pr,pϕ) up to order pr2/r4 included.
We develop a method for computing the linearized gravitational backreaction for Nambu-Goto strings using a fully covariant formalism. We work with equations of motion expressed in terms of a higher ...dimensional analog of the geodesic equation subject to self-generated forcing terms. The approach allows arbitrary spacetime and world sheet gauge choices for the background and perturbation. The perturbed spacetime metric may be expressed as an integral over a distributional stress-energy tensor supported on the string world sheet. By formally integrating out the distribution, this quantity may be reexpressed in terms of an integral over the retarded image of the string. In doing so, one must pay particular attention to contributions that arise from the field point and from nonsmooth regions of the string. Then, the gradient of the perturbed metric decomposes into a sum of boundary and bulk terms. The decomposition depends upon the world sheet coordinates used to describe the string, but the total is independent of those considerations. We illustrate the method with numerical calculations of the self-force at every point on the world sheet for loops with kinks, cusps and self-intersections using a variety of different coordinate choices. For field points on smooth parts of the world sheet the self-force is finite. As the field point approaches a kink or cusp the self-force diverges, but is integrable in the sense that the displacement of the world sheet remains finite. As a consistency check, we verify that the period-averaged flux of energy-momentum at infinity matches the direct work the self-force performs on the string. The methodology can be applied to address many fundamental questions for string loop evolution.
Motivated by applications to the study of self-force effects in scalar-tensor theories of gravity, we calculate the self-force exerted on a scalar charge in a circular orbit about a ...Reissner-Nordström black hole. We obtain the self-force via a mode-sum calculation and find that our results differ from recent post-Newtonian calculations even in the slow-motion regime. We compute the radiative fluxes toward infinity and down the black hole and verify that they are balanced by energy dissipated through the local self-force-in contrast to the reported post-Newtonian results. The self-force and radiative fluxes depend solely on the black hole’s charge-to-mass ratio, the controlling parameter of the Reissner-Nordström geometry. They both monotonically decrease as the black hole approaches extremality. With respect to an extremality parameter ε, the energy flux through the event horizon is found to scale as ∼ε5/4 as ε→0.
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