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We provide a geometric framework for the construction of non-vacuum black holes whose metrics are stationary and axisymmetric. Under suitable assumptions we show that the Einstein equations reduce to an Einstein-harmonic map type system and…
The evidence for the existence of dark matter in the universe is reviewed. A general picture emerges, where both baryonic and non-baryonic dark matter is needed to explain current observations. In particular, a wealth of observational…
The present work investigates some exact solutions of the gravitational wave equation in some widely used cosmological spacetimes. The examples are taken from spatially flat and closed isotropic models as well as Kasner metric which is…
These lectures have been given to particle physicists, mostly experimentalists and very briefly and at a pedestrian level review the problems of dark matter. The content of the lectures is the following: 1. Introduction. 2. Cosmological…
This work explores both classical and quantum aspects of an axisymmetric black hole within a non-commutative gauge theory. The rotating solution is derived using a modified Newman-Janis procedure. The analysis begins with the horizon…
The new 4D geometry whose Killing vectors span the Poincar\'e algebra is presented and its structure is analyzed. The new geometry can be regarded as the Poincar\'e-invariant solution of the degenerate extension of the vacuum Einstein field…
A new magnetically charged Kiselev black hole solution is used to study the null geodesics in this spacetime. We derive the equations of motion for the null geodesics and analyze their properties, including the gravitational lensing effect.…
Within the framework of the Einstein's standard equations of the general theory of relativity, flat galactic rotational curves of galaxies cannot be explained without hypothesis attracting the dark matter, the particles of which had not yet…
In the presence of a Killing symmetry, various self-gravitating field theories with massless scalars (moduli) and vector fields reduce to sigma-models, effectively coupled to 3-dimensional gravity. We argue that this particular structure of…
In the framework of non-riemannian geometry, we derive exact static vacuum solutions of the field equations obtained from the full equivalent version of the Einstein-Hilbert action when torsion degrees of freedom are taken into account. By…
In this paper, we present new axisymmetric and reflection symmetric vacuum solutions to the Einstein field equations. They are obtained using the Hankel integral transform method and all three solutions exhibit naked singularities. Our…
This contribution intends to give a pedagogical introduction to the topic of dark energy (the mysterious agent supposed to drive the observed late time acceleration of the Universe) and to various observational tests which require only…
Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…
We discuss universal properties of axisymmetric and stationary configurations consisting of a central black hole and surrounding matter in Einstein-Maxwell theory. In particular, we find that certain physical equations and inequalities…
The search for solutions of Einstein's equations representing relativistic cosmological models with a discrete matter content has been remarkably fruitful in the last decade. In this review we discuss the progress made in the study of a…
We consider plane-symmetric spacetimes satisfying Einstein's field equations with positive cosmological constant, when the matter is a fluid whose pressure is equal to its mass-energy density (i.e. a so-called stiff fluid). We study the…
We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on…
In this article we find a four-dimensional metric for a large black hole immersed in dark matter. Specifically, we look for and find a static spherically symmetric black hole solution to the Einstein equations which gives, in the Newtonian…
We characterize a general solution to the vacuum Einstein equations which admits isolated horizons. We show it is a non-linear superposition -- in precise sense -- of the Schwarzschild metric with a certain free data set propagating…
We study Einstein's equations with matter in hydrostatic equilibrium in the nonstandard gauge which was recently investigated in the vacuum case. We obtain spherically symmetric solutions for any given rotation curve. These solutions can be…