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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.
A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at null infi
After a short review of prominent properties of gravitational waves and the newly born gravitational astronomy, we focus on theoretical aspects. Analytic approximation methods in general relativity have played a crucial role in the recent discoveries
Gravitational-wave sources offer us unique testbeds for probing strong-field, dynamical and nonlinear aspects of gravity. In this chapter, we give a brief overview of the current status and future prospects of testing General Relativity with gravitat
We present the first numerical relativity waveforms for binary black hole mergers produced using spectral methods that show both the displacement and the spin memory effects. Explicitly, we use the SXS Collaborations $texttt{SpEC}$ code to run a Cauc
Gravitational waves deliver information in exquisite detail about astrophysical phenomena, among them the collision of two black holes, a system completely invisible to the eyes of electromagnetic telescopes. Models that predict gravitational wave si