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Register a new userGWsim: a code to simulate gravitational waves propagating in a potential well
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Jian-Hua He
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We present a code to simulate the propagation of GWs in a potential well in the time domain. Our code uses the finite element method (FEM) based on the publicly available code {it deal.ii}. We test our code using a point source monochromatic spherical wave. We examine not only the waveform observed by a local observer but also the global energy conservation of the waves. We find that our numerical results agree with the analytical predictions very well. Based on our code, we study the propagation of the leading wavefront of GWs in a potential well. We find that our numerical results agree with the results obtained from tracing null geodesics very well. Based on our simulations, we also test the accuracy of the thin-lens model in predicting the positions of the wavefront. We find that the analytical formula of the Shapiro-time delay is only accurate in regimes that are far away from the center of the potential well. However, near the optic axis, the analytical formula shows significant differences from the simulated ones. Besides these results, we find that unlike the conventional images in geometric optics, GWs can not be sheltered by the scatterer due to wave effects. The signals of GWs can circle around the scatterer and travel along the optic axis until arrive at a distant observer, which is an important observational consequence in such a system.
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The grand challenges of contemporary fundamental physics---dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem---all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress.
Circularly polarized gravitational sandwich waves exhibit, as do their linearly polarized counterparts, the Velocity Memory Effect: freely falling test particles in the flat after-zone fly apart along straight lines with constant velocity. In the inside zone their trajectories combine oscillatory and rotational motions in a complicated way. For circularly polarized periodic gravitational waves some trajectories remain bounded, while others spiral outward. These waves admit an additional screw isometry beyond the usual five. The consequences of this extra symmetry are explored.
We give an account of the gravitational memory effect in the presence of the exact plane wave solution of Einsteins vacuum equations. This allows an elementary but exact description of the soft gravitons and how their presence may be detected by observing the motion of freely falling particles. The theorem of Bondi and Pirani on caustics (for which we present a new proof) implies that the asymptotic relative velocity is constant but not zero, in contradiction with the permanent displacement claimed by Zeldovich and Polnarev. A non-vanishing asymptotic relative velocity might be used to detect gravitational waves through the velocity memory effect, considered by Braginsky, Thorne, Grishchuk, and Polnarev.
The direct detection of gravitational waves now provides a new channel of testing gravity theories. Despite that the parametrized post-Einsteinian framework is a powerful tool to quantitatively investigate effects of modification of gravity theory, the gravitational waveform in this framework is still extendable. One of such extensions is to take into account the gradual activation of dipole radiation due to massive fields, which are still only very weakly constrained if their mass $m$ is greater than $10^{-16}$ eV from pulsar observations. Ground-based gravitational-wave detectors, LIGO, Virgo, and KAGRA, are sensitive to this activation in the mass range, $10^{-14}$ eV $lesssim m lesssim 10^{-13}$ eV. Hence, we discuss a dedicated test for dipole radiation due to a massive field using the LIGO-Virgo collaborations open data. In addition, assuming Einstein-dilaton-Gauss-Bonnet (EdGB) type coupling, we combine the results of the analysis of the binary black hole events to obtain the 90% confidence level constraints on the coupling parameter $alpha_{rm EdGB}$ as $sqrt{alpha_{rm EdGB}} lesssim 2.47$ km for any mass less than $6 times 10^{-14}$ eV for the first time, including $sqrt{alpha_{rm EdGB}} lesssim 1.85$ km in the massless limit.
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