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Primordial gravitational waves are a crucial prediction of inflation theory, and their detection through their imprints on the cosmic microwave background is actively being pursued. However, these attempts have not yet been successful. In…
In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed in a generalized sense. The applications included the…
These lecture notes provide a brief introduction to methods used to search for a stochastic background of gravitational radiation -- a superposition of gravitational-wave signals that are either too weak or too numerous to individually…
In the harmonic description of general relativity, the principle part of Einstein equations reduces to a constrained system of 10 curved space wave equations for the components of the space-time metric. We use the pseudo-differential theory…
Gravitational waves (GW) are expected to interact with dark energy and dark matter, affecting their propagation on cosmological scales. In order to model this interaction, we derive a gauge invariant effective equation and action valid for…
Gravitational waves, first predicted by Albert Einstein within the framework of general relativity, were confirmed in 2015 by the LIGO/Virgo collaboration, marking a pivotal breakthrough in astrophysics. Despite this achievement, a key…
We consider the Einstein-Boltzmann system for massless particles in the Bianchi I space-time with scattering cross-sections in a certain range of soft potentials. We assume that the space-time has an initial conformal gauge singularity and…
Hydromagnetic turbulence produced during phase transitions in the early universe can be a powerful source of stochastic gravitational waves (GWs). GWs can be modelled by the linearised spatial part of the Einstein equations sourced by the…
Cylindrical gravitational waves of Einstein gravity are described by an integrable system (Ernst system) whose quantization is a long standing problem. We propose to bootstrap the quantum theory along the following lines: The quantum theory…
We describe the properties of evanescent gravitational waves (EGWs)---wave solutions of Einstein equations which decay exponentially in some direction while propagating in another. Evanescent waves are well-known in acoustics and optics and…
We study gravitational waves to first and second order in amplitude in vacuum asymptotically flat spacetimes. The Einstein equations are solved to first order and these solutions are superposed to form a time-symmetric ingoing and then…
We discuss the initial value problem of general relativity in its recently unified Lagrangian and Hamiltonian pictures and present a multi-domain pseudo-spectral collocation method to solve the resulting coupled nonlinear partial…
A world-wide array of highly sensitive interferometers stands poised to usher in a new era in astronomy with the first direct detection of gravitational waves. The data from these instruments will provide a unique perspective on extreme…
Fully non-linear, plane-symmetric exact solutions of the Einstein equations describing the scattering of gravitational and electromagnetic waves have existed for many years. For these closed-form solutions to be found, idealized wave…
A stochastic background of gravitational waves can be created by the superposition of a large number of independent sources. The physical processes occurring at the earliest moments of the universe certainly created a stochastic background…
The starting point of this work is the original Einstein action, sometimes called the Gamma squared action. Continuing from our previous results, we study various modified theories of gravity following the Palatini approach. The metric and…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled…
An epoch of matter domination in the early universe can enhance the primordial stochastic gravitational wave signal, potentially making it detectable to upcoming gravitational wave experiments. However, the resulting gravitational wave…
We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for…