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We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a…
We try to lay down the foundations of a Newtonian theory where inertia and gravitational fields appear in a unified way aiming to reach a better understanding of the general relativistic theory. We also formulate a kind of equivalence…
We linearize the Einstein equations when the metric is Bondi-Sachs, when the background is Schwarzschild or Minkowski, and when there is a matter source in the form of a thin shell whose density varies with time and angular position. By…
We provide a simple derivation of the Schwarzschild solution in General Relativity, generalizing an early approach by Weyl, to include Birkhoff's theorem: constancy of the mass; its deeper, Hamiltonian, basis is also given. Our procedure is…
A simple general relativity theory for objects moving in gravitational fields is developed based on studying the behavior of an atom in a gravitational field. The theory is applied to calculate the satellite time dilation, light deflection…
A class of exact conformastatic solutions of the Einstein-Maxwell field equations is presented in which the gravitational and electromagnetic potentials are completely determined by a harmonic function only. The motion of test particles is…
Both massless light ray and objects with nonzero mass experience trajectory bending in a gravitational field. In this work the bending of trajectories of massive objects in a Schwarzschild spacetime and the corresponding gravitational…
We present the manifestly covariant Lagrangian of a massless polarized particle, that implies all dynamic and algebraic equations as the conditions of extreme of this variational problem. The model allows for minimal interaction with a…
Exact time-dependent solutions of Einstein's gravitational field equation for a spherical mass moving with arbitrarily high constant velocity are derived and analyzed. The threshold conditions required for gravitational repulsion of…
We present a time-dependent solution of the Maxwell equations in the Einstein universe, whose electric and magnetic fields, as seen by the stationary observers, are aligned with the Clifford parallels of the $3$-sphere $S^3$. The conformal…
Starting from the action function, we have derived a theoretical background that leads to the quantization of gravity and the deduction of a correlation between the gravitational and the inertial masses, which depends on the kinetic…
We present, in closed analytic form, a general stationary, slowly rotating black hole, which is solution to a large class of alternative theories of gravity in four dimensions. In these theories, the Einstein-Hilbert action is supplemented…
The description of relativistic effects requires a preliminary definition of events localised in space-time while the clocks used for time definition and the fields used in synchronisation or localisation procedures are necessarily quantum…
It is shown that Einstein-Rosen bridges (wormholes) hypothetical objects that topologically connect separate locations in the Universe can be static solutions of the Einstein equations. The corresponding equations for bridges are reduced to…
A modification to the vis-viva equation that accounts for general relativistic effects is introduced to enhance the accuracy of predictions of orbital motion and precession. The updated equation reduces to the traditional vis-viva equation…
The field equations of general relativity can be derived from the Einstein action, which is quadratic in connection coefficients, rather than the standard action involving the Gibbons-Hawking-York term and counterterm. We show that it is…
In the context of investigations of possible highly relativistic motions of a spinning particle in the gravitational field, which can be described by the Mathisson equations under different supplementary condition, we analyze the circular…
The content of Einstein's theory of gravitation is encoded in the properties of the solutions to his field equations. There has been obtained a wealth of information about these solutions in the ninety years the theory has been around. It…
We present equations of motion for charged particles using balanced equations, and without introducing explicitly divergent quantities. This derivation contains as particular cases some well known equations of motion, as the Lorentz-Dirac…
The study investigates orbital motion of test particles near compact objects described by solutions involving massless scalar fields, electromagnetic fields, and nonlinear electrodynamics. Specifically, we analyze orbital dynamics in the…