Related papers: On Integrating the Left-Flat Vacuum Einstein Equat…
A new approach to the two-body problem based on the extension of the $SL(2,C)$ group to the $Sp(4,C)$ one is developed. The wave equation with the Lorentz-scalar and Lorentz-vector potential interactions for the system of one spin-1/2 and…
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We…
Integrable quantum mechanical systems for neutral particles with spin $\frac12$ and nontrivial dipole momentum are classified. It is demonstrated that such systems give rise to new exactly solvable problems of quantum mechanics with clear…
In this paper, we explore static spherically symmetric wormhole solutions in the framework of $n$-dimensional Einstein Gauss-Bonnet gravity. Our objective is to find out wormhole solutions that satisfy energy conditions. For this purpose,…
Solutions to the Einstein equation that represent the superposition of static isolated bodies with axially symmetry are presented. The equations nonlinearity yields singular structures (strut and membranes) to equilibrate the bodies. The…
We present a set of three PDEs for three real scalars that are equivalent to the full Einstein equations without any symmetry assumptions. The main variables in this formulation are null surfaces and a conformal factor. Furthermore, for…
An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect fluid solutions of Einstein's equations. For physically relevant…
The paper develops a $(2+2)$-imbedding formalism adapted to a double foliation of spacetime by a net of two intersecting families of lightlike hypersurfaces. The formalism is two-dimensionally covariant, and leads to simple, geometrically…
We classify solutions of the vacuum weighted Einstein field equations on smooth metric measure spacetimes $(M,g,h\, dvol_g)$ of dimension 4, where the underlying manifold $(M,g)$ is a $pr$-wave. We use this result to provide examples of…
We obtain an exact solution for the Einstein's equations with cosmological constant coupled to a scalar, static particle in static, "spherically" symmetric background in 2+1 dimensions.
In the semiclassical approximation of Grassmann-valued electric charges for regularizing Coulomb self-energies, we extract the unique acceleration-independent interaction hidden in any Lienard-Wiechert solution for the system of N…
Spin Foam Models (SFMs) are covariant formulations of Loop Quantum Gravity (LQG) in 4 dimensions. This work studies the perturbations of SFMs on a flat background. It demonstrates for the first time that smooth curved spacetime geometries…
All Lorentz invariant solutions of vacuum Einstein's equations are found. It is proved that these solutions describe space-times of constant curvature.
The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical…
We classify up to automorphisms all left-invariant non-Einstein solutions to the Einstein--Maxwell equations on 4-dimensional Lie algebras.
We solve the constraint equations for a vacuum space-time with a translational space-like Killing field satisfying the vacuum Einstein equations. Vacuum Einstein equations with a translational space-like Killing field have been studied by…
Following a solution generating technique introduced recently by one of us, we transform the Einstein static Universe into a two - fold infinity class of physically acceptable exact perfect fluid solutions of Einstein's equations. Whereas…
This article introduces the notions of asymptotic dust and asymptotic radiation equations of state. With these non-linear generalizations of the well known dust or (incoherent) radiation equations of state the perfect-fluid equations loose…
It is well-known that the Einstein-Rosen solutions to the 3+1 dimensional vacuum Einstein's equations are in one to one correspondence with solutions of 2+1 dimensional general relativity coupled to axi-symmetric, zero rest mass scalar…
This paper deals with an extension of a previous work [Gravitation & Cosmology, Vol. 4, 1998, pp 107--113] to exact spherical symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of…