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The future detection of gravitational wave forces us to consider the many ways in which astrophysics, gravitational wave theory and fundamental theory will interact. In this paper, I summarize some recent work done to develop such an…
This review is focused on tests of Einstein's theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein's theory has been greatly constrained in the…
In these lecture notes I review the theory of the non--linear evolution of cosmological perturbations in a self--gravitating collisionless medium, with vanishing vorticity. The problem is first analyzed in the context of the Newtonian…
We establish a generic, fully-relativistic formalism to study gravitational-wave emission by extreme-mass-ratio systems in spherically-symmetric, non-vacuum black-hole spacetimes. The potential applications to astrophysical setups range…
We provide analysis to determine the effects of gravitational waves on electromagnetic waves, using perturbation theory in general relativity. Our analysis is performed in a completely covariant manner without invoking any coordinates. For…
A special conformal transformation which carries a vacuum gravitational wave into another vacuum one is built by using M\"obius-redefined time. It can either transform a globally defined vacuum wave into a vacuum sandwich wave, or carry the…
The cosmological propagation of tensor perturbations is studied in the context of parity-violating extensions of the symmetric teleparallel equivalent of General Relativity theory. This non-Riemannian formulation allows for a wider variety…
We study the numerical propagation of waves through future null infinity in a conformally compactified spacetime. We introduce an artificial cosmological constant, which allows us some control over the causal structure near null infinity.…
"Acoustic spacetimes", in which techniques of differential geometry are used to investigate sound propagation in moving fluids, have attracted considerable attention over the last few decades. Most of the models currently considered in the…
In this manuscript we review the theoretical foundations of gravitational waves in the framework of Albert Einstein's theory of general relativity. Following Einstein's early efforts we first derive the linearised Einstein field equations…
The interferometry-based experimental tests of quantum properties of space-time which the author sketched out in a recent short Letter [Nature 398 (1999) 216] are here discussed in self-contained fashion. Besides providing detailed…
The modeling of gravitational wave ringdown has traditionally relied on linear perturbation theory, which mainly describes the late-time behavior of a perturbed black hole after a binary merger. However, the need for more accurate ringdown…
In the weak-field limit of General Relativity, gravitational waves obey linear equations and propagate at the speed of light. These properties of General Relativity are supported by the observation of ultra high energy cosmic rays as well…
The question whether gravitational waves are quantised or not can in principle be answered by the help of correlation measurements. If the gravitational waves are quantised and they are generated by the change of the background metrics then…
We study the gravitational waves in spacetimes of arbitrary dimension. They generalize the pp-waves and the Kundt waves, obtained earlier in four dimensions. Explicit solutions of the Einstein and Einstein-Maxwell equations are derived for…
In the weak field regime, gravitational waves can be considered as being made up of collisionless, relativistic tensor modes that travel along null geodesics of the perturbed background metric. We work in this geometric optics picture to…
These notes provide a student-friendly introduction to the theory of gravitational waves in full, non-linear general relativity (GR). We aim for a balance between physical intuition and mathematical rigor and cover topics such as the…
The detection of gravitational waves (GWs) propagating through cosmic structures can provide invaluable information on the geometry and content of our Universe, as well as on the fundamental theory of gravity. In order to test possible…
We investigate gravitational radiation in the linear approximation within the framework of the recent nonlocal generalization of Einstein's theory of gravitation. In this theory, nonlocality can simulate dark matter; in fact, in the…
The recent observation of gravitational waves, stimulates the question of the longtime evolution of the space-time fluctuations. Gravitational waves interact themselves through the nonlinear character of Einstein's equations of general…