Abstract:
The present work aims to search for an implementation of new symmetries in the space-time in order to enable us to find a connection between electrodynamics and gravitation, from where quantum principles naturally emerge. To do that, first of all we build a heuristic model of the electromagnetic nature of the electron so that the influence of the gravitational field on the electrodynamics of such moving particle leads us essentially to an elimination of the classical idea of rest by introducing the idea of a universal minimum limit of speed ($V$). Such a lowest limit $V$, being unattainable by the particles, represents a fundamental and preferred reference frame connected to a universal background field (a vacuum energy) that breaks Lorentz symmetry. So there emerges a new principle of symmetry in the space-time at the subatomic level for very low energies close to the background frame ($v\approx V$), providing a fundamental understanding for the uncertainty principle.

Abstract:
The influence of spin in a system of classical particles on the propagation of gravitational waves is analyzed in the cosmological context of primordial thermal equilibrium. On a flat Friedmann-Robertson-Walker metric, when the precession is neglected, there is no contribution due to the spin to the distribution function of the particles. Adding a small tensor perturbation to the background metric, we study if a coupling between gravitational waves and spin exists that can modify the evolution of the distribution function, leading to new terms in the anisotropic stress, and then to a new source for gravitational waves. In the chosen gauge, the final result is that, in the absence of other kind of perturbations, there is no coupling between spin and gravitational waves.

Abstract:
Various authors have investigated the problem of light deflection by radially moving gravitational lenses - with inconsistent results. In this paper we generalize the calculations for arbitrary lens velocities and show that, to first order in the lens velocity v, the deflection angles scales with 1-v. We discuss the seeming inconsistency of relativistic light deflection with the classical picture of moving test particles by generalizing the lens effect to test particles of arbitrary velocity, including light as a limiting case. We show that the effect of radial motion of the lens is very different for slowly moving test particles and light and that a critical test particle velocity exists for which the motion of the lens has no effect on the deflection angle to first order. An interesting and not immediately intuitive result is obtained in the limit of a highly relativistic motion of the lens towards the observer, where the deflection angle of light reduces to zero. This phenomenon is elucidated in terms of moving refractive media. Furthermore, we discuss the dragging of inertial frames in the field of a moving lens and the corresponding Lense-Thirring precession, in order to shed more light on the geometrical effects in the surroundings of a moving mass. In a second part we discuss the effect of transversal motion on the observed redshift of lensed sources. We demonstrate how a simple kinematic calculation explains the effects for arbitrary velocities of the lens and test particles. Additionally we include the transversal motion of the source and observer to show that all three velocities can be combined into an effective relative transversal velocity similar to the approach used in microlensing studies.

Abstract:
We study a mechanism to produce the circular polarization of primordial gravitational waves. The circular polarization is generated during the super-inflation driven by the Gauss-Bonnet term in the string-inspired cosmology. The instability in the tensor mode caused by the Gauss-Bonnet term and the parity violation due to the gravitational Chern-Simons term are the essential ingredients of the mechanism. We also discuss detectability of the produced circular polarization of gravitational waves. It turns out that the simple model of single-field inflation contradicts CMB observations. To circumvent this difficulty, we propose a two-field inflation model. In this two-field model, the circular polarization of gravitational waves is created in the frequency range designed by the Big-Bang Observer (BBO) or the deci-hertz gravitational-wave observatory (DECIGO).

Abstract:
What are gravitational waves? How do they propagate? and what is their energy content? These questions are addressed in the first two chapters. In the third chapter the pseudo-Newtonian formalism and its extension is reviewed in general and the formula for the momentum imparted to test particles in arbitrary spacetimes is reviewed in particular. In chapter four the analysis of a paper claiming to determine the spin for gravitational waves is given, and compared with the spin given by a geodesic analysis. It is demonstrated that the other claim is inconsistent. Finally in chapter five a summary of the work is given with the conclusion.

Abstract:
The Mathisson-Papapetrou-Dixon equations for a massive spinning test particle in plane gravitational waves are analysed and explicit solutions constructed in terms of solutions of certain linear ordinary differential equations. For harmonic waves this system reduces to a single equation of Mathieu-Hill type. In this case spinning particles may exhibit parametric excitation by gravitational fields. For a spinning test particle scattered by a gravitational wave pulse, the final energy-momentum of the particle may be related to the width, height, polarisation of the wave and spin orientation of the particle.

Abstract:
Using the Teukolsky and Sasaki-Nakamura formalisms for the perterbations around a Kerr black hole, we calculate the energy flux of gravitational waves induced by a {\it spinning} particle of mass $\mu$ and spin $S$ moving in circular orbits near the equatorial plain of a rotating black hole of mass $M (\gg \mu)$ and spin $Ma$. The calculations are performed by using the recently developed post-Newtonian expansion technique of the Teukolsky equation. To evaluate the source terms of perturbations caused by a {\it spinning} particle, we used the equations of motion of a spinning particle derived by Papapetrou and the energy momentum tensor of a spinning particle derived by Dixon. We present the post-Newtonian formula of the gravitational wave luminosity up to the order $(v/c)^5$ beyond the quadrupole formula including the linear order of particle spin. The results obtained in this paper will be an important guideline to the post-Newtonian calculation of the inspiral of two spinning compact objects.

Abstract:
The motion of a classical spinning test particle in the field of a weak plane gravitational wave is studied. It is found that the characteristic dimensions of the particle's orbit is sensitive to the ratio of the spin to the mass of the particle. The results are compared with the corresponding motion of a particle without spin.

Abstract:
We develop a numerical code to compute gravitational waves induced by a particle moving on eccentric inclined orbits around a Kerr black hole. For such systems, the black hole perturbation method is applicable. The gravitational waves can be evaluated by solving the Teukolsky equation with a point like source term, which is computed from the stress-energy tensor of a test particle moving on generic bound geodesic orbits. In our previous papers, we computed the homogeneous solutions of the Teukolsky equation using a formalism developed by Mano, Suzuki and Takasugi and showed that we could compute gravitational waves efficiently and very accurately in the case of circular orbits on the equatorial plane. Here, we apply this method to eccentric inclined orbits. The geodesics around a Kerr black hole have three constants of motion: energy, angular momentum and the Carter constant. We compute the rates of change of the Carter constant as well as those of energy and angular momentum. This is the first time that the rate of change of the Carter constant has been evaluated accurately. We also treat the case of highly eccentric orbits with $e=0.9$. To confirm the accuracy of our codes, several tests are performed. We find that the accuracy is only limited by the truncation of $\ell$-, $k$- and $n$-modes, where $\ell$ is the index of the spin-weighted spheroidal harmonics, and $n$ and $k$ are the harmonics of the radial and polar motion, respectively. When we set the maximum of $\ell$ to 20, we obtain a relative accuracy of $10^{-5}$ even in the highly eccentric case of $e=0.9$. The accuracy is better for lower eccentricity. Our numerical code is expected to be useful for computing templates of the extreme mass ratio inspirals, which is one of the main targets of the Laser Interferometer Space Antenna (LISA).

Abstract:
In two-dimensional space-time, point particles can experience a geometric, dimension-specific gravity force, which modifies the usual geodesic equation of motion and provides a link between the cosmological constant and the vacuum $\theta$-angle. The description of such forces fits naturally into a gauge theory of gravity based on the extended Poincar\'e group, {\it i.e.\/} ``string-inspired'' dilaton gravity.