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Register a new userIndirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs
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The Regge-Wheeler-Zerilli (RWZ) wave-equation describes Schwarzschild-Droste black hole perturbations. The source term contains a Dirac distribution and its derivative. We have previously designed a method of integration in time domain. It consists of a finite difference scheme where analytic expressions, dealing with the wave-function discontinuity through the jump conditions, replace the direct integration of the source and the potential. Herein, we successfully apply the same method to the geodesic generic orbits of EMRI (Extreme Mass Ratio Inspiral) sources, at second order. An EMRI is a Compact Star (CS) captured by a Super Massive Black Hole (SMBH). These are considered the best probes for testing gravitation in strong regime. The gravitational wave-forms, the radiated energy and angular momentum at infinity are computed and extensively compared with other methods, for different orbits (circular, elliptic, parabolic, including zoom-whirl).
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We apply our method of indirect integration, described in Part I, at fourth order, to the radial fall affected by the self-force. The Mode-Sum regularisation is performed in the Regge-Wheeler gauge using the equivalence with the harmonic gauge for this orbit. We consider also the motion subjected to a self-consistent and iterative correction determined by the self-force through osculating stretches of geodesics. The convergence of the results confirms the validity of the integration method. This work complements and justifies the analysis and the results appeared in Int. J. Geom. Meth. Mod. Phys., 11, 1450090 (2014).
Bound geodesic orbits around a Kerr black hole can be parametrized by three constants of the motion: the (specific) orbital energy, angular momentum and Carter constant. Generically, each orbit also has associated with it three frequencies, related to the radial, longitudinal and (mean) azimuthal motions. Here we note the curious fact that these two ways of characterizing bound geodesics are not in a one-to-one correspondence. While the former uniquely specifies an orbit up to initial conditions, the latter does not: there is a (strong-field) region of the parameter space in which pairs of physically distinct orbits can have the same three frequencies. In each such isofrequency pair the two orbits exhibit the same rate of periastron precession and the same rate of Lense-Thirring precession of the orbital plane, and (in a certain sense) they remain synchronized in phase.
For a stationary, axisymmetric, asymptotically flat, ultra-compact [$i.e.$ containing light-rings (LRs)] object, with a $mathbb{Z}_2$ north-south symmetry fixing an equatorial plane, we establish that the structure of timelike circular orbits (TCOs) in the vicinity of the equatorial LRs, for either rotation direction, depends exclusively on the stability of the LRs. Thus, an unstable LR delimits a region of unstable TCOs (no TCOs) radially above (below) it; a stable LR delimits a region of stable TCOs (no TCOs) radially below (above) it. Corollaries are discussed for both horizonless ultra-compact objects and black holes. We illustrate these results with a variety of exotic stars examples and non-Kerr black holes, for which we also compute the efficiency associated with converting gravitational energy into radiation by a material particle falling under an adiabatic sequence of TCOs. For most objects studied, it is possible to obtain efficiencies larger than the maximal efficiency of Kerr black holes, $i.e.$ larger than $42%$.
The detection of gravitational wave signals by Advanced LIGO and Advanced Virgo enables us to probe the polarization content of gravitational waves. In general relativity, only tensor modes are present, while in a variety of alternative theories one can also have vector or scalar modes. Recently test were performed which compared Bayesian evidences for the hypotheses that either purely tensor, purely vector, or purely scalar polarizations were present. Indeed, with only three detectors in a network and allowing for mixtures of tensor polarizations and alternative polarization states, it is not possible to identify precisely which non-standard polarizations might be in the signal and by what amounts. However, we demonstrate that one can still infer whether, in addition to tensor polarizations, alternative polarizations are present in the first place, irrespective of the detailed polarization content. We develop two methods to do this for sources with electromagnetic counterparts, both based on the so-called null stream. Apart from being able to detect mixtures of tensor and alternative polarizations, these have the added advantage that no waveform models are needed, and signals from any kind of transient source with known sky position can be used. Both formalisms allow us to combine information from multiple sources so as to arrive at increasingly more stringent bounds. For now we apply these on the binary neutron star signal GW170817, showing consistency with the tensor-only hypothesis with p-values of 0.315 and 0.790 for the two methods.
We present a null-stream-based Bayesian unmodeled framework to probe generic gravitational-wave polarizations. Generic metric theories allow six gravitational-wave polarization states, but general relativity only permits the existence of two of them namely the tensorial polarizations. The strain signal measured by an interferometer is a linear combination of the polarization modes and such a linear combination depends on the geometry of the detector and the source location. The detector network of Advanced LIGO and Advanced Virgo allows us to measure different linear combinations of the polarization modes and therefore we can constrain the polarization content by analyzing how the polarization modes are linearly combined. We propose the basis formulation to construct a null stream along the polarization basis modes without requiring modeling the basis explicitly. We conduct a mock data study and we show that the framework is capable of probing pure and mixed polarizations in the Advanced LIGO-Advanced Virgo 3-detector network without knowing the sky location of the source from electromagnetic counterparts. We also discuss the effect of the presence of the uncaptured orthogonal polarization component in the framework, and we propose using the plug-in method to test the existence of the orthogonal polarizations.
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