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Register a new userGravitational radiation and the evolution of gravitational collapse in cylindrical symmetry
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Using the Sparling form and a geometric construction adapted to spacetimes with a 2-dimensional isometry group, we analyse a quasi-local measure of gravitational energy. We then study the gravitational radiation through spacetime junctions in cylindrically symmetric models of gravitational collapse to singularities. The models result from the matching of collapsing dust fluids interiors with gravitational wave exteriors, given by the Einstein-Rosen type solutions. For a given choice of a frame adapted to the symmetry of the matching hypersurface, we are able to compute the total gravitational energy radiated during the collapse and state whether the gravitational radiation is incoming or outgoing, in each case. This also enables us to distinguish whether a gravitational collapse is being enhanced by the gravitational radiation.
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General cylindrical waves are the simplest axisymmetrical gravitational waves that contain both $+$ and $times$ modes of polarization. In this paper, we have studied the evolution of general cylindrical gravitational waves in the realm of the characteristic scheme with a numerical code based on the Galerkin-Collocation method. The investigation consists of the numerical realization of concepts such as Bondi mass and the news functions adapted to cylindrical symmetry. The Bondi mass decays due to the presence of the news functions associated with both polarization modes. We have interpreted that each polarization mode as channels from which mass is extracted. Under this perspective, we have presented the enhancement effect of the polarization mode $+$ due to the nonlinear interaction with the mode $times$. After discussing the role of matter in cylindrical symmetry, we have extended the numerical code to include electromagnetic fields.
We demonstrate that evolutions of three-dimensional, strongly non-linear gravitational waves can be followed in numerical relativity, hence allowing many interesting studies of both fundamental and observational consequences. We study the evolution of time-symmetric, axisymmetric {it and} non-axisymmetric Brill waves, including waves so strong that they collapse to form black holes under their own self-gravity. The critical amplitude for black hole formation is determined. The gravitational waves emitted in the black hole formation process are compared to those emitted in the head-on collision of two Misner black holes.
In the weak field approximation the gravitational wave is approximated as a linear wave, which ignores the nonlinear effect. In this paper, we present an exact general solution of the cylindrical gravitational wave. The exact solution of the cylindrical gravitational wave is far different from the weak field approximation. This solution implies the following conclusions. (1) There exist gravitational monopole radiations in the cylindrical gravitational radiation. (2) The gravitational radiation may generate the resonance in the spacetime. (3) The nonlinearity of the gravity source vanishes after time averaging, so the observed result of a long-time measurement may be linear.
We present a Galerkin-Collocation domain decomposition algorithm applied to the evolution of cylindrical unpolarized gravitational waves. We show the effectiveness of the algorithm in reproducing initial data with high localized gradients and in providing highly accurate dynamics. We characterize the gravitational radiation with the standard Newman-Penrose Weyl scalar $Psi_4$. We generate wave templates for both polarization modes, $times$ and $+$, outgoing and ingoing, to show how they exchange energy nonlinearly. In particular, considering an initially ingoing $times$ wave, we were able to trace a possible imprint of the gravitational analog of the Faraday effect in the generated templates.
We discuss the prospects of gravitational lensing of gravitational waves (GWs) coming from core-collapse supernovae (CCSN). As the CCSN GW signal can only be detected from within our own Galaxy and the local group by current and upcoming ground-based GW detectors, we focus on microlensing. We introduce a new technique based on analysis of the power spectrum and association of peaks of the power spectrum with the peaks of the amplification factor to identify lensed signals. We validate our method by applying it on the CCSN-like mock signals lensed by a point mass lens. We find that the lensed and unlensed signal can be differentiated using the association of peaks by more than one sigma for lens masses larger than 150 solar masses. We also study the correlation integral between the power spectra and corresponding amplification factor. This statistical approach is able to differentiate between unlensed and lensed signals for lenses as small as 15 solar masses. Further, we demonstrate that this method can be used to estimate the mass of a lens in case the signal is lensed. The power spectrum based analysis is general and can be applied to any broad band signal and is especially useful for incoherent signals.
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