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Register a new userDissipation in extreme-mass ratio binaries with a spinning secondary
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We present the gravitational-wave flux balance law in an extreme mass-ratio binary with a spinning secondary. This law relates the flux of energy (angular momentum) radiated to null infinity and through the event horizon to the local change in the secondarys orbital energy (angular momentum) for generic (non-resonant) bound orbits in Kerr spacetime. As an explicit example we compute these quantities for a spin-aligned body moving on a circular orbit around a Schwarzschild black hole. We perform this calculation both analytically, via a high-order post-Newtonian expansion, and numerically in two different gauges. Using these results we demonstrate explicitly that our new balance law holds.
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We calculate the evolution and gravitational-wave emission of a spinning compact object inspiraling into a substantially more massive (non-rotating) black hole. We extend our previous model for a non-spinning binary [Phys. Rev. D 93, 064024] to include the Mathisson-Papapetrou-Dixon spin-curvature force. For spin-aligned binaries we calculate the dephasing of the inspiral and associated waveforms relative to models that do not include spin-curvature effects. We find this dephasing can be either positive or negative depending on the initial separation of the binary. For binaries in which the spin and orbital angular momentum are not parallel, the orbital plane precesses and we use a more general osculating element prescription to compute inspirals.
We present an analytic computation of Detweilers 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 Detweilers redshift invariant, it can be readily extended to other gauge invariant quantities and to higher post-Newtonian orders.
Extreme-mass-ratio inspirals (EMRIs), compact binaries with small mass-ratios $epsilonll 1$, will be important sources for low-frequency gravitational wave detectors. Almost all EMRIs will evolve through important transient orbital $rtheta$-resonances, which will enhance or diminish their gravitational wave flux, thereby affecting the phase evolution of the waveforms at $O(epsilon^{1/2})$ relative to leading order. While modeling the local gravitational self-force (GSF) during resonances is essential for generating accurate EMRI waveforms, so far the full GSF has not been calculated for an $rtheta$-resonant orbit owing to computational demands of the problem. As a first step we employ a simpler model, calculating the scalar self-force (SSF) along $rtheta$-resonant geodesics in Kerr spacetime. We demonstrate two ways of calculating the $rtheta$-resonant SSF (and likely GSF), with one method leaving the radial and polar motions initially independent as if the geodesic is non-resonant. We illustrate results by calculating the SSF along geodesics defined by three $rtheta$-resonant ratios (1:3, 1:2, 2:3). We show how the SSF and averaged evolution of the orbital constants vary with the initial phase at which an EMRI enters resonance. We then use our SSF data to test a previously-proposed integrability conjecture, which argues that conservative effects vanish at adiabatic order during resonances. We find prominent contributions from the conservative SSF to the secular evolution of the Carter constant, $langle dot{mathcal{Q}}rangle$, but these non-vanishing contributions are on the order of, or less than, the estimated uncertainties of our self-force results. The uncertainties come from residual, incomplete removal of the singular field in the regularization process. Higher order regularization parameters, once available, will allow definitive tests of the integrability conjecture.
Extreme-Mass-Ratio Inspirals (EMRIs) are one of the most promising sources of gravitational waves (GWs) for space-based detectors like the Laser Interferometer Space Antenna (LISA). EMRIs consist of a compact stellar object orbiting around a massive black hole (MBH). Since EMRI signals are expected to be long lasting (containing of the order of hundred thousand cycles), they will encode the structure of the MBH gravitational potential in a precise way such that features depending on the theory of gravity governing the system may be distinguished. That is, EMRI signals may be used to test gravity and the geometry of black holes. However, the development of a practical methodology for computing the generation and propagation of GWs from EMRIs in theories of gravity different than General Relativity (GR) has only recently begun. In this paper, we present a parameter estimation study of EMRIs in a particular modification of GR, which is described by a four-dimensional Chern-Simons (CS) gravitational term. We focus on determining to what extent a space-based GW observatory like LISA could distinguish between GR and CS gravity through the detection of GWs from EMRIs.
In the context of metric perturbation theory for non-spinning black holes, extreme mass ratio binary (EMRB) systems are described by distributionally forced master wave equations. Numerical solution of a master wave equation as an initial boundary value problem requires initial data. However, because the correct initial data for generic-orbit systems is unknown, specification of trivial initial data is a common choice, despite being inconsistent and resulting in a solution which is initially discontinuous in time. As is well known, this choice leads to a burst of junk radiation which eventually propagates off the computational domain. We observe another unintended consequence of trivial initial data: development of a persistent spurious solution, here referred to as the Jost junk solution, which contaminates the physical solution for long times. This work studies the influence of both types of junk on metric perturbations, waveforms, and self-force measurements, and it demonstrates that smooth modified source terms mollify the Jost solution and reduce junk radiation. Our concluding section discusses the applicability of these observations to other numerical schemes and techniques used to solve distributionally forced master wave equations.
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