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The dark matter problem is one of the most pressing problems in modern physics. As there is no well-established claim from a direct detection experiment supporting the existence of the illusive dark matter that has been postulated to…
A number of recent observations have suggested that the Einstein's theory of general relativity may not be the ultimate theory of gravity. The f(R) gravity model with R being the scalar curvature turns out to be one of the best bet to…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity.…
We argue that the conjectured dark mater in the Universe may be endowed with a new kind of gravitational charge that couples to a short range gravitational interaction mediated by a massive vector field. A model is constructed that…
We consider solutions with conformal symmetry of the static, spherically symmetric gravitational field equations in the vacuum in the brane world scenario. By assuming that the vector field generating the symmetry is non-static, the general…
The Universe could be spatially flat, positively curved or negatively curved. Each option has been popular at various times, partly affected by an understanding that models tend to evolve away from flatness. The curvature of the Universe is…
We explore the possibility that the entire departure of galactic rotational velocities from their luminous Newtonian expectation be cosmological in origin, and show that within the framework of conformal gravity (but not Einstein gravity…
We argue that Einstein gravity coupled to a Born-Infeld theory provides an attractive candidate to represent dark matter and dark energy. For cosmological models, the Born-Infeld field has an equation of state which interpolates between…
We construct a novel class of spherically symmetric and asymptotically flat black holes and naked singularities surrounded by anisotropic dark matter fluid with the equation of state (EoS) of the form $P_t=\omega \rho$. We assume that dark…
The Einstein postulates assert an invariance of the propagation speed of light in vacuum for any observer, and which amounts to a presumed absence of any preferred frame. The postulates appear to be directly linked to relativistic effects…
We define the stretched future light cone, a timelike hypersurface composed of the worldlines of radially accelerating observers with constant and uniform proper acceleration. By attributing temperature and entropy to this hypersurface, we…
We find a new family of galactic metrics corresponding to flat rotation curves at the outer radii. These are vacuum solutions to a gravity theory where the Newton's coupling varies mildly in space. The effective `mass', whose origin is…
In the previous work, we investigated the rotation curves of galaxies assuming that the dark matter consists of ultra light boson appearing in $'$late time phase transition' theory. Generalizing this work, we consider the effect of visible…
I present an alternative explanation of flat rotational curves of galaxies that does not require dark matter but rather relies on classical Newtonian dynamics and an overlooked effect of quantum tunneling. I introduce a rotational drag…
A review is given of a priori predictions made for the dynamics of rotating galaxies. One theory - MOND - has had many predictions corroborated by subsequent observations. While it is sometimes possible to offer post hoc explanations for…
We investigate the gravitational lensing effect around a spherically symmetric black hole, whose metric is obtained from the Einstein field equation with electric charge and perfect-fluid dark matter contributing to its energy-momentum…
We consider the possibility of an alternative gravity theory explaining the dynamics of galactic systems without dark matter. From very general assumptions about the structure of a relativistic gravity theory we derive a general expression…
Dark matter is one of the deepest mystery of the universe. So far there is no natural explanation why the dark matter should exist and even dominate the universe. In this paper, we begin with a 3+1D topological gravity theory which is super…
The solution of Einstein's field equations in Cosmological General Relativity (CGR), where the Galaxy is at the center of a finite yet bounded spherically symmetrical isotropic gravitational field, is identical with the unbounded solution.…