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Register a new userPersistent junk solutions in time-domain modeling of extreme mass ratio binaries
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Scott E. Field n Brown
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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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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.
A powerful technique to calculate gravitational radiation from binary systems involves a perturbative expansion: if the masses of the two bodies are very different, the small body is treated as a point particle of mass $m_p$ moving in the gravitational field generated by the large mass $M$, and one keeps only linear terms in the small mass ratio $m_p/M$. This technique usually yields finite answers, which are often in good agreement with fully nonlinear numerical relativity results, even when extrapolated to nearly comparable mass ratios. Here we study two situations in which the point-particle approximation yields a divergent result: the instantaneous flux emitted by a small body as it orbits the light ring of a black hole, and the total energy absorbed by the horizon when a small body plunges into a black hole. By integrating the Teukolsky (or Zerilli/Regge-Wheeler) equations in the frequency and time domains we show that both of these quantities diverge. We find that these divergences are an artifact of the point-particle idealization, and are able to interpret and regularize this behavior by introducing a finite size for the point particle. These divergences do not play a role in black-hole imaging, e.g. by the Event Horizon Telescope.
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.
We present analytic computations of gauge invariant quantities for a point mass in a circular orbit around a Schwarzschild black hole, giving results up to 15.5 post-Newtonian order in this paper and up to 21.5 post-Newtonian order in an online repository. Our calculation is based on the functional series method of Mano, Suzuki and Takasugi (MST) and a recent series of results by Bini and Damour. We develop an optimised method for generating post-Newtonian expansions of the MST series, enabling significantly faster computations. We also clarify the structure of the expansions for large values of $ell$, and in doing so develop an efficient new method for generating the MST renormalised angular momentum, $ u$.
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.
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