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In this article, I present an elementary introduction to the theory of gravitational waves. This article is meant for students who have had an exposure to general relativity, but, results from general relativity used in the main discussion…
A new type of fluid matter model in general relativity is introduced, in which the fluid particles are subject to velocity diffusion without friction. In order to compensate for the energy gained by the fluid particles due to diffusion, a…
The averaging problem in general relativity is briefly discussed. A new setting of the problem as that of macroscopic description of gravitation is proposed. A covariant space-time averaging procedure is described. The structure of the…
In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are…
Numerical relativity is an essential tool for solving Einstein's equations of general relativity for dynamical systems characterized by high velocities and strong gravitational fields. The implementation of new algorithms that can solve…
We consider static massive thin cylindrical shells (tubes) as the sources in Einstein's equations. They correspond to $\dl$- and $\dl'$-function type energy-momentum tensors. The corresponding metric components are found explicitly. They…
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…
A conservative extension of general relativity by integrable Weyl geometry is formulated, and a new class of cosmological models ({\em Weyl universes}) is introduced and studied. A short discussion of how these new models behave in the…
In this paper I investigate the possibility to test Einstein's equations with observations of cosmological large scale structure. I first show that we have not tested the equations in observations concerning only the homogeneous and…
Notes prepared for the introductory general relativity course PHYSICS 748 at The University of Auckland. They are designed to introduce general relativity to upper-year undergraduate students directly using the modern language of…
Galilean Relativity and Einstein's Special and General Relativity showed that the Laws of Physics go deeper than their representations in any given reference frame. Thus covariance, or independence of Laws of Physics with respect to changes…
The most simple observed cases of gravitational lensing of distant quasars and galaxies by galaxies and clusters of galaxies are used to test Einstein's theory of General Relativity and Newtonian Gravity over galactic and intergalactic…
This paper aims to provide teachers with a tool to teach the essential features of special relativity, considering the students' difficulties highlighted by numerous studies. Our proposal presents special relativity as the solution to the…
General relativity describes gravitation in terms of the geometry of spacetime. It predicts the existence of gravitational waves (GWs) that stretch and compress spacetime and were detected recently by state-of-the-art interferometer…
While there are many applications of ML to scientific problems that look promising, visuals can be deceiving. Using numerical analysis techniques, we rigorously quantify the accuracy, convergence rates, and generalization bounds of certain…
A new class of exact solutions of the Einstein-Maxwell system is found in closed form. This is achieved by choosing a generalised form for one of the gravitational potentials and a particular form for the electric field intensity. For…
Electromagnetic observations have been used over the past decades to understand the nature of black holes and the material around them. Our ability to learn about the fundamental physics relies on our understanding of two key ingredients in…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
We attempt to see how closely we can formally obtain the planetary and light path equations of General Relativity by employing certain operations on the familiar Newtonian equation. This article is intended neither as an alternative to nor…
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…