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Along the lines of the Einstein-Rosen wave equation of General Relativity (GR), we derive a gravitational wave equation with cylindrical symmetry in the Einstein-aether (EA) theory. We show that the gravitational wave in the EA is periodic…
Using the Einstein gravitation theory we show how to obtain the basic equations which predict the gravitational waves. This paper was written to graduate and post-graduate students of Physics. We deduce the equations didactically following…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple two layers star model: a self-gravitating ball built up by two layers of perfect fluid having different linear…
We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to the Einstein's linearized field equations. We show that only the Ricci squared quadratic invariant contributes to…
We combine Maxwell's equations with Eulers's equation, related to a velocity field of an immaterial fluid, where the density of mass is replaced by a charge density. We come out with a differential system able to describe a relevant…
Einstein's equations in matter are gravitational analogues of Maxwell's equations in matter, providing an effective classical description of gravitational fields. We derive Einstein's equations in matter for relativistic fluids, and use…
In this paper, we investigate whether Variational Principles can be associated with the Helmholtz equation subject to impedance (absorbing) boundary conditions. This model has been extensively studied in the literature from both…
In the middle of last century, Bondi and his coworkers proposed an out going boundary condition for the Einstein equations. Based on such boundary condition the authors theoretically solved the puzzle of the existence problem of…
The known exact solutions of Einstein's vacuum field equations modeling the gravitational fields of pure gravitational radiation involve wave fronts which are either planar or roughly spherical. We describe a scheme designed to check…
Taking into account the mass transfer effect, we derive the equations of motion of a compact binary system at the second-half post-Newtonian order. Applying such equations of motion to quasi-circular orbits, we obtain the time derivative of…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
A new formulation is presented for a variational calculation of $N$-body systems on a correlated Gaussian basis with arbitrary angular momenta. The rotational motion of the system is described with a single spherical harmonic of the total…
We present an exact, time-dependent solution for the Einstein field equations that models the coupling between an anisotropic fluid and a magnetic field in an axially symmetric space-time. By carefully selecting the metric components, we…
The effective gravitational mass as well as the energy and momentum distributions of a radiating charged particle in Einstein's universe are evaluated. The Moller's energy-momentum complex is employed for this computation. The spacetime…
It is proposed that the equations of motion in periodic relativity which yielded major predictions of general relativity are exact in nature and can be applied to pulsars and inspiraling compact binaries for analyzing orbital period…
We consider the conformal wave equation on the Einstein cylinder with a defocusing cubic non-linearity. Motivated by a method developed by Rostworowski-Maliborski on the existence of time periodic solutions to the spherically symmetric…
The gravitational constant variation means the breakdown of the strong equivalence principle. As the cornerstone of general relativity, the validity of general relativity can be examined by studying the gravitational constant variation.…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
We use the basic equations that predict the emission of gravitational waves according to the Einstein gravitation theory to calculate the luminosities and the amplitudes of the waves generated by binary stars, pulsations of neutron stars,…