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It has long been known that Newtonian dynamics applied to the visible matter in galaxies and clusters does not correctly describe the dynamics of those systems. While this is generally taken as evidence for dark matter it is in principle…
The relativistic fluid is a highly successful model used to describe the dynamics of many-particle, relativistic systems. It takes as input basic physics from microscopic scales and yields as output predictions of bulk, macroscopic motion.…
The hypothesis that the Lorentz transformations may be modified at Planck scale energies is further explored. We present a general formalism for theories which preserve the relativity of inertial frames with a non-linear action of the…
This brief review is intended to introduce gravitational physicists to recent developments in which general relativity is being used to describe certain aspects of condensed matter systems, e.g., superconductivity.
We have observed the acceleration of the expansion of the universe. To explain this phenomenon, we usually introduce the dark energy (DE) which has a negative pressure or we need to modify the Einstein's equation to produce a term which is…
The Cardassian universe is a proposed modification to the Friedmann equation in which the universe is flat, matter dominated, and accelerating. In the ordinary Friedmann equation, the right hand side is a linear function of the energy…
An exact solution of Einstein's field equations for a static spherically symmetric medium with a radially boost invariant energy-momentum tensor is presented. In the limit of an equation of state corresponding to a distribution of radially…
Recently, several interesting proposals were made modifying the law of gravity on large scales, within a sensible relativistic formulation. This allows a precise formulation of the idea that such a modification might account for galaxy…
Hartle's model provides the most widely used analytic framework to describe isolated compact bodies rotating slowly in equilibrium up to second order in perturbations in the context of General Relativity. Apart from some explicit…
CRESST is a direct dark matter search experiment, aiming for an observation of nuclear recoils induced by the interaction of dark matter particles with cryogenic scintillating calcium tungstate crystals. Instead of confining ourselves to…
The Hamilton-Lagrange action principle for Relativistic Schr\"odinger Theory (RST) is converted to a variational principle (with constraints) for the stationary bound states. The groundstate energy is the minimally possible value of the…
The forthcoming Stage-IV experiments aim to map the large scale structure of the Universe at high precision. The scales explored require a relativistic description, in addition to statistical tools for their analysis. In this thesis, we…
This is the third paper by Nordstr{\"o}m on his five dimensional theory. Here Nordstr{\"o}m attempts to base a theory of matter on the energy conservation generalized to the five dimensional case. This involves a new fundamental constant…
The $\Lambda$CDM framework offers a remarkably good description of our universe with a very small number of free parameters, which can be determined with high accuracy from currently available data. However, this does not mean that the…
The discovery of accelerated cosmic expansion implies that, in addition to the attractive gravity of matter, there exists in our universe some other form of energy (dark energy or cosmological constant) producing a repulsive force. The…
The developments summarized with the name ``weak gravitational lensing'' have led to exciting possibilities to study the (statistical properties of the) dark matter distribution in the Universe. Concentrating on those aspects which require…
In this article, we will review Noether's Theorems and their application in General Relativity. We will present Noether's Theorems in their original form and restate them as they are usually applied to physics. Some basic equations of…
The relativistic conservation law involving the center of energy is reviewed and illustrated using simple examples from classical electromagnetic theory. It is emphasized that this conservation law is parallel to the conservation laws for…
It is shown that a first-order relativistic perturbation theory for the open, flat or closed Friedmann-Lemaitre-Robertson-Walker universe admits one, and only one, gauge-invariant quantity which describes the perturbation to the energy…
For physicists, recent developments in astrophysics and cosmology present exciting challenges. We are conducting "experiments" in energy regimes some of which will be probed by accelerators in the near future, and others which are…