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We show how to derive the equations of light propagation in the gravitational field of uniformly moving mass monopoles without formulating and integrating the differential equations of light propagation in that field. The well-known…
We discuss the propagation of gravitational waves in a recently discussed class of theories containing N >= 2 metric tensors and a corresponding number of standard model copies. Using the formalism of gauge-invariant linear perturbation…
We describe "small bodies" in a non-metric gravity theory previously studied by this author. The main dynamical field of the theory is a certain triple of two-forms rather than the metric, with only the spacetime conformal structure, not…
In the Newtonian limit of $f(R)$ gravity, for an isolated self-gravitating system consisting of $N$ extended fluid bodies, the inter-body dynamics are studied by applying the symmetric and trace-free formalism in terms of irreducible…
The present paper studies the post-Newtonian dynamics of N bodies in general relativity. We derive covariant equations of translational and rotational motion of N extended bodies having arbitrary distribution of mass and velocity of matter…
Following the formalism of enveloping algebras and star product calculus we formulate and analyze a model of gauge gravity on noncommutative spaces and examine the conditions of its equivalence to general relativity. The corresponding…
Applying Dixon's general equations of motion for extended bodies, we compute the Papapetrou's equations for an extended test body on static and isotropic metrics. We incorporate the force and the torque terms which involve multipole…
The motion of massless spinning test particles is investigated using the Newman-Penrose formalism within the Mathisson-Papapetrou model extended to massless particles by Mashhoon and supplemented by the Pirani condition. When the "multipole…
In this thesis, multipole expansions of mass, momentum and stress density will be made for a body in Newtonian mechanics. Using these definitions; momentum, angular momentum, center of mass, force and torque are defined for $N$…
In this paper we consider equations of motion for 2-body problem according to an observer close to one of the gravitational bodies. The influence of the Thomas precession of the observer's frame has an important role. The equations of…
We study theories of gravity with non-minimal coupling between polarized media with pole-dipole and quadrupole moments and an arbitrary function of the space-time curvature scalar $R$ and the squares of the Ricci and Riemann curvature…
Motion of massive and massless test particle in equilibrium and non-equilibrium case is discussed in a dyadosphere geometry through Hamilton-Jacobi method. Geodesics of particles are discussed through Lagrangian method too. Scalar wave…
Using post-Newtonian equations of motion for fluid bodies valid to the second post-Newtonian order, we derive the equations of motion for binary systems with finite-sized, non-spinning but arbitrarily shaped bodies. In particular we study…
The dynamics of extended bodies is a fundamental problem in any gravitational theory. In the case of General Relativity, this problem is under study since the theory was published. Several methods have been developed and different…
In contrast to electrodynamics, Einstein's gravitation equations are not invariant with respect to a wide class of the mapping of field variables which leave equations of motion of test particles in a given coordinate system invariant. It…
We describe gauge theories which allow to retrieve a large class of gravitational theories, including, MacDowell-Mansouri gravity and its topological extension to Loop Quantum Gravity via the Pontrjagin characteristic class involving the…
The spacetime evolution of massless spinning particles in a Robertson-Walker background is derived using the deterministic system of equations of motion due to Papapetrou, Souriau and Saturnini. A numerical integration of this system of…
We formulate elasticity theory with microrotations using the framework of gauge theories, which has been developed and successfully applied in various areas of gravitation and cosmology. Following this approach, we demonstrate the existence…
The dynamics of "dipolar particles", i.e. particles endowed with a four-vector mass dipole moment, is investigated using an action principle in general relativity. The action is a specific functional of the particle's world line, and of the…
We consider the motion of small bodies in general relativity. The key result captures a sense in which such bodies follow timelike geodesics (or, in the case of charged bodies, Lorentz-force curves). This result clarifies the relationship…