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It is nowadays clear that General Relativity cannot be the definitive theory of Gravitation due to several shortcomings that come out both from theoretical and experimental viewpoints. At large scales (astrophysical and cosmological) the…
We give a pedagogical introduction of the essential features of General Theory of Relativity (GTR) in the format of an undergraduate (UG) project. A set of simple MATHEMATICA code is developed which enables the UG students to calculate the…
Transformation equations for the kinetic energy of the same bullet in Galileo's and Einstein's special relativity are derived. The special relativity result is extended to the case of a photon.
In this contribution we deal with several issues one encounters when trying to couple quantum matter to classical gravitational fields. We start with a general background discussion and then move on to two more technical sections. In the…
We derive new representations of the Einstein-Hilbert action in which graviton perturbation theory is immensely simplified. To accomplish this, we recast the Einstein-Hilbert action as a theory of purely cubic interactions among gravitons…
Recent studies have thrown up a big enigma. On the one hand they point to satellite galaxies rotating faster than they should with the usual theory. On the other hand they also go against explanation of Newtonian gravity with dark matter.…
We give precise details to support that observations of gravitational lensing at scales of individual, groups and clusters of galaxies can be understood in terms of non-Newtonian gravitational interactions with a relativistic structure…
This lecture note covers Relativistic Kinematics, which is very useful for the beginners in the field of high-energy physics. A very practical approach has been taken, which answers "why and how" of the kinematics useful for students…
Some useful kinematical relations for the absorption of a photon by a nucleus and its recoil are derived for the relativistic incident energies. These expressions provided for the relativistic kinematics of photoabsorption reactions, though…
In this article, we develop a formalism which is different from the standard lensing scenario and is necessary for understanding lensing by gravitational fields which arise as solutions of the effective Einstein equations on the brane. We…
Exact stationary axially symmetric solutions of the 4D Einstein equations with corotating pressureless perfect fluid sources are studied. A particular solution with approximately flat rotation curve is discussed in some detail. We find that…
The theory of evolution equations has been applied in various ways in general relativity. Following some general considerations about this, some illustrative examples of the use of ordinary differential equations in general relativity are…
Statements about relativistic effects are often subtle. In this essay we will demonstrate that the three classical tests of general relativity, namely perihelion precession, deflection of light and gravitational redshift, are passed…
The problem of explaining the acceleration of the expansion of the universe and the observational and theoretical difficulties associated with dark matter and dark energy are discussed. The possibility that Einstein gravity does not…
A generalization of General Relativity is studied. The standard Einstein-Hilbert action is considered in the Palatini formalism, where the connection and the metric are independent variables, and the connection is not symmetric. As a result…
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…
We study the non-relativistic expansion of general relativity coupled to matter. This is done by expanding the metric and matter fields analytically in powers of $1/c^2$ where $c$ is the speed of light. In order to perform this expansion it…
Correct and complete (to terms of $\vec{v} / c$ -- $\vec{v}$ is particle's velocity, $c$ is the speed of light) derivation of equation of motion for real dust particle under the action of electromagnetic radiation is derived. The effect of…
It is well known that the Einstein-Hilbert action in two dimensions is topological and yields an identically vanishing Einstein tensor. Consequently one is faced with difficulties when formulating a non-trivial gravity model. We present a…
With continuous advances in technologies related to deep space ranging and satellite gravity gradiometry, corrections from general relativity to the dynamics of relative orbital motions will certainly become important. In this work, we…