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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…
The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface $Z$ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations…
We study the utilization of conformal compactification within the conformal approach to solving the constraints of general relativity for asymptotically flat initial data. After a general discussion of the framework, particular attention is…
The energy and momentum transported by exact plane gravitational-wave solutions of Einstein equations are computed using the teleparallel equivalent formulation of Einstein's theory. It is shown that these waves transport neither energy nor…
For gravitational-wave spacetimes of Shapovalov type III, exact general solutions of geodesic deviation equations and equations of motion of test particles are obtained. Solutions are found in a privileged coordinate system, where the…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
As a first step in exploring time-periodic solutions of the Einstein equations with a negative cosmological constant, we study the cubic conformal wave equation on the Einstein cylinder. Using a combination of numerical and perturbative…
We establish a well-posedness theory for the f(R) theory of modified gravity, which is a generalization of Einstein's theory of gravitation. The scalar curvature R of the spacetime, which arises in the integrand of the Einstein-Hilbert…
The behaviour of a "test" electromagnetic field in the background of an exact gravitational plane wave is investigated in the framework of Einstein's general relativity. We have expressed the general solution to the de Rham equations as a…
The response of a gravitational wave detector to scalar waves is analysed in the framework of the debate on the choice of conformal frames for scalar-tensor theories. A correction to the geodesic equation arising in the Einstein conformal…
For nearly a century, Einstein's theory of gravity has been the standard theory for describing gravitational phenomena in our universe. Along with its successes, limitations of the theory from theoretical (e.g., singularities) and…
We propose a way to construct manifestly gauge independent quantities out of the gauge dependent quantities occurring in the linearized Einstein equations. Thereupon, we show that these gauge-invariant combinations can be identified with…
The Einstein equations in wave map gauge are a geometric second order system for a Lorentzian metric. To study existence of solutions of this hyperbolic quasi diagonal system with initial data on a characteristic cone which are not zero in…
This dissertation consists of four parts. In Part I, we briefly review fundamental theories of gravity, performed experimental tests, and gravitational waves. The framework and the methods that we use in our calculations are discussed in…
This is the first of a series of papers describing a numerical implementation of the conformally rescaled Einstein equation, an implementation designed to calculate asymptotically flat spacetimes, especially spacetimes containing black…
Data from gravitational wave detectors are recorded as time series that include contributions from myriad noise sources in addition to any gravitational wave signals. When regularly sampled data are available, such as for ground based and…
Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications these models are incomplete, which both reduces the prospects of…
As is well-known, the Schwarzschild metric cannot be derived based on pre-general-relativistic physics alone, which means using only special relativity, the Einstein equivalence principle and the Newtonian limit. The standard way to derive…
We consider the space-condensate inflation model to study the primordial gravitational waves generated in the early Universe. We calculate the energy spectrum of gravitational waves induced by the space-condensate inflation model for full…
Waves in excitable media can be treated by a simple geometric theory. The propagation velocity is assumed known and evolution of wave fronts is determined by elementary physical principles (Fermat's principle, Huygens' principle). Based on…