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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 fundamental metrics, which describe any static three-dimensional Einstein-Maxwell spacetime (depending only on a unique spacelike coordinate), are found. In this case there are only three independent components of the electromagnetic…
We propose a model describing Einstein gravity coupled to a scalar field with an exponential potential. We show that the weak-field limit of the model has static solutions given by a gravitational potential behaving for large distances as…
The electromagnetic theory is considered in the framework of the generally covariant approach, that is applied to the analysis of electromagnetism in noninertial coordinate and frame systems. The special-relat\-ivistic formulation of…
I present a new method to generate rotating solutions of the Einstein--Maxwell equations from static solutions, and briefly discuss its general properties.
We analyze linear Einstein--Maxwell perturbations of the superextremal Reissner--Nordstr\"om geometry in its static Kerr--Schild rest frame, viewing it as the nonlinear self-field of a single static point charge. In optical radial…
Under a particular choice of the Ernst potential, we solve analytically the Einstein-Maxwell equations to derive a new exact solution depending on five parameters: the mass, the angular-momentum (per unit mass), the electromagnetic-field…
It is shown that the pre-metric approach to Maxwell's equations provides an alternative to the traditional Einstein-Maxwell unification program, namely, that electromagnetism and gravitation are unified in a different way that makes the…
A particular yet large class of non-diverging solutions which admits a cosmological constant, electromagnetic field, pure radiation and/or general non-null matter component is explicitly presented. These spacetimes represent exact…
We found new class of solutions to the Einstein-Maxwell system of equations for charged quark matter within the framework of MIT Bag Model considering a gravitational potential Z(x) proposed by Thirukkanesh and Ragel (2013), which depends…
We study properties of a recently proposed new ansatz for separation of variables in the Maxwell equations in four dimensional Kerr-NUT-(A)dS spacetime. We demonstrate that a dual field, which is also a solution of the source-free Maxwell…
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…
Physically admissible choice of the "essential" coordinates identified with components of the metric tensor and co-moving frame of reference reduced to the formulation of the stationary axisymmetric GR problem. Such nontraditional approach…
The theory of gauge transformations in linearized gravitation is investigated. After a brief discussion of the fundamentals of the kinetic theory in curved spacetime, the Einstein-Vlasov-Maxwell system of equations in terms of gauge…
In a series of articles we describe a novel class of geometrical models of relativistic stars. Our approach to the static spherically symmetric solutions of Einstein equations is based on a careful physical analysis of radial gauge…
A unification of Klein--Gordon, Dirac, Maxwell, Rarita--Schwinger and Einstein equations exact solutions (for the massless fields cases) is presented. The method is based on writing all of the relevant dynamical fields in terms of products…
A formulation of Einstein's gravitational field equations in four space-time dimensions is presented using generalized differential forms and Cartan's equations for metric geometries. Cartan's structure equations are extended by using…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
The field equations in modified gravity theories possess an important decoupling property with respect to certain classes of nonholonomic frames. This allows us to construct generic off--diagonal solutions depending on all spacetime…
A model is proposed for the classical electron as a point charge with finite electromagnetic self-energy. Modifications of the Reissner-Nordstr{\o}m (spin 0) and Kerr-Newman (spin 1/2) solutions of the Einstein-Maxwell equations are…