[en] We present numerical evolutions of three equal-mass black holes using the moving puncture approach. We calculate puncture initial data for three black holes solving the constraint equations by means of a high-order multigrid elliptic solver. Using these initial data, we show the results for three black hole evolutions with sixth-order waveform convergence. We compare results obtained with the BAM and AMSS-NCKU codes with previous results. The approximate analytic solution to the Hamiltonian constraint used in previous simulations of three black holes leads to different dynamics and waveforms. We present some numerical experiments showing the evolution of four black holes and the resulting gravitational waveform.

[en] Testing the equivalence principle (EP) is of great importance for fundamental physics. Whether the EP is held for dark matter (DM) is still unclear. Motivated by the recent discoveries of gravitational waves (GWs) by ground based detectors, we study the possibility of testing EP of DM by GW experiments. We consider a binary composed of a black hole (BH) and a neutron star (NS) with respect to the galactic DM as the attractor. Possibly, long-range fifth-force other than gravity between DM and ordinary matter may lead to the EP violation for DM, we investigate the effect of fifth-force acted by DM on the GW waveform of the BH-NS binary. The presence of the fifth-force will lead to a phase correction in the GW waveform which may be detectable, but the phase correction depends chaotically on the initial condition. We calculate the probability of detection for different initial conditions. The probability depends on the time interval of integration, the EP-violating driving force and the initial eccentricity. We find for appropriate conditions the probability can reach to a considerable value, and even approach to 1 in some extremal cases. For example, for most BH-NS binaries formed in the field locating as far as the solar system to the galactic center, the fifth force with the Eötvös parameter ${\mathrm{\eta <!--\; ??\; -->}}_{\text{DM}}^{\text{BH},\text{NS}}⩾<!--\; ???\; -->0.01$ will result in the probability of detection >0.6 if the interval of integral time is from f = 1 Hz to the final state when the NS is disrupted by the BH. These predictions may be tested by future GW observations. (paper)

[en] Neutron stars may sustain a non-axisymmetric deformation due to magnetic distortion and are potential sources of continuous gravitational waves (GWs) for ground-based interferometric detectors. With decades of searches using available GW detectors, no evidence of a GW signal from any pulsar has been observed. Progressively stringent upper limits of ellipticity have been placed on Galactic pulsars. In this work, we use the ellipticity inferred from the putative millisecond magnetars in short gamma-ray bursts (SGRBs) to estimate their detectability by current and future GW detectors. For ∼1 ms magnetars inferred from the SGRB data, the detection horizon is ∼30 Mpc and ∼600 Mpc for the advanced LIGO (aLIGO) and Einstein Telescope (ET), respectively. Using the ellipticity of SGRB millisecond magnetars as calibration, we estimate the ellipticity and GW strain of Galactic pulsars and magnetars assuming that the ellipticity is magnetic-distortion-induced. We find that the results are consistent with the null detection results of Galactic pulsars and magnetars with the aLIGO O1. We further predict that the GW signals from these pulsars/magnetars may not be detectable by the currently designed aLIGO detector. The ET detector may be able to detect some relatively low-frequency signals (<50 Hz) from some of these pulsars. Limited by its design sensitivity, the eLISA detector seems to not be suitable for detecting the signals from Galactic pulsars and magnetars.

[en] Based on spin weighted spherical harmonic decomposition, the $(2,\pm <!--\; ??\; -->2)$ modes dominate the gravitational waveforms generated by binary black holes. Several recent works found that other modes including $(l,0)$ ones are also important to gravitational wave data analysis. For aligned-spin binaries, these $(l,0)$ modes are related to the memory effect of gravitational wave. Based on the post-Newtonian analysis, quasi-normal modes analysis and the results of numerical relativity simulations, we present a full inspiral-merger-ringdown gravitational waveform model for the $(2,0)$ mode generated by binary black holes. Our model includes the quasinormal ringing part and includes the effect of a black hole’s spin. It is complementary to the previous results. (paper)

[en] A new scheme for computing dynamical evolutions and gravitational radiations for intermediate-mass-ratio inspirals (IMRIs) based on an effective one-body (EOB) dynamics plus Teukolsky perturbation theory is built in this paper. In the EOB framework, the dynamic essentially affects the resulted gravitational waveform for a binary compact star system. This dynamic includes two parts. One is the conservative part, which comes from effective one-body reduction. The other part is the gravitational backreaction, which contributes to the shrinking process of the inspiral of a binary compact star system. Previous works used an analytical waveform to construct this backreaction term. Since the analytical form is based on post-Newtonian expansion, the consistency of this term is always checked by numerical energy flux. Here, we directly use numerical energy flux by solving the Teukolsky equation via the frequency-domain method to construct this backreaction term. The conservative correction to the leading order terms in mass-ratio is included in the deformed-Kerr metric and the EOB Hamiltonian. We try to use this method to simulate not only quasicircular adiabatic inspiral, but also the nonadiabatic plunge phase. For several different spinning black holes, we demonstrate and compare the resulted dynamical evolutions and gravitational waveforms.

[en] The coalescence of a stellar-mass compact object together with an intermediate-mass black hole, also known as an intermediate-mass-ratio inspiral, is usually not expected to be a viable gravitational wave source for the current ground-based gravitational wave detectors, due to the generally lower frequency of such a source. In this paper, we adopt the effective-one-body formalism as the equation of motion, and obtain the accurately calculated gravitational waveforms by solving the Teukolsky equation using the frequency-domain method. We point out that high frequency modes of gravitational waves can be excited by large eccentricities of intermediate-mass-ratio inspirals. These high frequency modes can extend to more than 10 Hz, and enter the designed sensitive band of Advanced LIGO and Advanced Virgo. We propose that such kinds of highly eccentric intermediate-mass-ratio inspirals could be feasible sources and potentially observable by the ground-based gravitational wave detectors, like the Advanced LIGO and Advanced Virgo. (paper)

[en] Starting from the Kerr–Schild coordinates, a set of horizon penetrating harmonic coordinates for the Kerr metric is worked out and exhibit the explicit form of the whole metric. As a validity check on the calculations, the multipole expansion of the Kerr metric is then derived from the harmonic formulation. The resemblance of the geometry of the harmonic slicing with the ‘1 + log’ slicing and the generalized harmonic gauge in numerical relativity is then further discussed. Together with its horizon penetrating structure, the harmonic formulation is well suited for the numerical simulation of astrophysical electromagnetic phenomena, like for instance the Blanford–Znajek process, in the vicinity of a supermassive black hole. (note)

[en] We report on our code, in which the moving puncture method is applied and an adaptive/fixed mesh refinement is implemented, and on its preliminary performance on black hole simulations. Based on the Baumgarte-Sharpiro-Shibata-Nakamura (BSSN) formulation, up-to-date gauge conditions and the modifications of the formulation are also implemented and tested. In this work, we present our primary results about the simulation of a single static black hole, of a moving single black hole, and of the head-on collision of a binary black hole system. For the static punctured black hole simulations, different modifications of the BSSN formulation are applied. It is demonstrated that both the currently used sets of modifications lead to a stable evolution. For cases of a moving punctured black hole with or without spin, we search for viable gauge conditions and study the effect of spin on the black hole evolution. Our results confirm previous results obtained by other research groups. In addition, we find a new gauge condition, which has not yet been adopted by any other researchers, which can also give stable and accurate black hole evolution calculations. We examine the performance of the code for the head-on collision of a binary black hole system, and the agreement of the gravitational waveform it produces with that obtained in other works. In order to understand qualitatively the influence of matter on the binary black hole collisions, we also investigate the same head-on collision scenarios but perturbed by a scalar field. The numerical simulations performed with this code not only give stable and accurate results that are consistent with the works by other numerical relativity groups, but also lead to the discovery of a new viable gauge condition, as well as clarify some ambiguities in the modification of the BSSN formulation. These results demonstrate that this code is reliable and ready to be used in the study of more realistic astrophysical scenarios and of numerical relativity.

[en] Recently, inwardly propagating waves (called antiwaves, AWs) in nonlinear oscillatory systems have attracted much attention. An interesting negative refraction phenomenon has been observed in a bidomain system where one medium supports forwardly propagating waves (normal waves, NWs) and the other AWs. In this paper we find that negative refraction (NR) in nonlinear media has an asymmetric property, i.e., NR can be observed only by applying wave source with proper frequency to one medium, but not the other. Moreover, NR appears always when the incident waves are dense and the refractional waves are sparse. This asymmetry is a particular feature for nonlinear NR, which can neither be observed in linear refraction processes (both positive and negative refractions) nor in nonlinear positive refraction. The mechanism underlying the asymmetry of nonlinear NR are fully understood based on the competition of nonlinear waves.

[en] The purpose of this note is to clarify the conditions under which the first-order generalize-harmonic representation of the vacuum Einstein evolution system is linearly degenerate. (note)