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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…
One of the longstanding problems of modern gravitational physics is the detection of gravitational waves, for which the standard theoretical analysis relies upon the split of the space-time metric into a background metric plus perturbation.…
A solution of linearized Einstein field equations in vacuum is given and discussed. First it is shown that, computing from our particular metric the linearized connections, the linearized Riemann tensor and the linearized Ricci tensor, the…
We describe a new method for extracting gravitational wave signals from pulsar timing data. We show that any gravitational wave signal can be decomposed into an orthogonal set of sky maps, with the number of maps equal to the number of…
The group theoretical approach to the relativistic wave equations on the real reducible spaces for spin~0, 1/2 and~1 massless particles is considered. The invariant wave equations which determine the appropriate irreducible representations…
Deviation equation: Second order differential equation for the 4-vector which measures the distance between reference points on neighboring world lines in spacetime manifolds. Relativistic geodesy: Science representing the Earth (or any…
We derive gravitational waves in a theory with non-local curvature corrections to the Hilbert-Einstein Lagrangian. In addition to the standard two massless tensor modes, with plus and cross polarizations, helicity 2 and angular frequency…
The tidal effects generated by a nonlinear gravitational wave are investigated in double-null v - u coordinates, as an exact solution of Einstein's field equations. The components $\xi^{v}$ and $\xi^{u}$ of the separation vector behave as…
We analyze the polarization structure of gravitational waves in the framework of Extended Relativity (ER), using the deviation tensor as the fundamental observable quantity. Starting from the point-source solution, we derive the radiation…
We study the gravitational field of a spinning radiation beam-pulse in a higher dimensional spacetime. We derive first the stress-energy tensor for such a beam in a flat spacetime and find the gravitational field generated by it in the…
The relative motion of a classical relativistic spinning test particle is studied with respect to a nearby free test particle in the gravitational field of a rotating source. The effects of the spin-curvature coupling force are elucidated…
We derive the perturbation equations for relativistic stars in scalar-tensor theories of gravity and study the corresponding oscillation spectrum. We show that the frequency of the emitted gravitational waves is shifted proportionally to…
We find the explicit forms of the anti-de Sitter plane, anti-de Sitter spherical, and pp waves that solve both the linearized and exact field equations of the most general higher derivative gravity theory in three dimensions. As a…
The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…
We construct the gravitational energy-momentum pseudo-tensor of up to fourth-order conformally invariant theories of gravity. Then we linearize the pseudo-tensor and use its average over a macroscopic region to find the energy and momentum…
The construction of exact linearized solutions to the Einstein equations within the Bondi-Sachs formalism is extended to the case of linearization about de Sitter spacetime. The gravitational wave field measured by distant observers is…
Gravitational-wave astronomy provides a promising avenue for the discovery of new physics beyond general relativity as it probes extreme curvature and ultra-relativistic dynamics. However, in the absence of a compelling alternative to…
The detection of primordial gravitational waves would offer a direct evidence of inflation and valuable insights into the dynamics of the early universe. During post-inflation reheating period, when the inflaton coherently oscillates at the…
The geometry of impulsive pp-waves is explored via the analysis of the geodesic and geodesic deviation equation using the distributional form of the metric. The geodesic equation involves formally ill-defined products of distributions due…
In a previous article [Phys. Rev. D 82 104040 (2010)], we derived an energy-momentum tensor for linear gravity that exhibited positive energy density and causal energy flux. Here we extend this framework by localizing the angular momentum…