Related papers: A technique for generating new solutions of Einste…
A generation procedure, based on the 5-dimensional covariance of the Kaluza-Klein theory, is developed. The procedure allows one to obtain exact solutions of the 4-dimensional Einstein equations with electromagnetic and scalar fields from…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
We introduce a semiclassical Einstein-Langevin equation as a consistent dynamical equation for a first order perturbative correction to semiclassical gravity. This equation includes the lowest order quantum stress-energy fluctuations of…
We present a first attempt to apply the approach of deformation quantization to linearized Einstein's equations. We use the analogy with Maxwell equations to derive the field equations of linearized gravity from a modified Maxwell…
We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been…
In this article, we achieved several non-naturally reductive Einstein metrics on exceptional simple Lie groups, which are formed by the decomposition arising from general Wallach spaces. By using the decomposition corresponding to the two…
We derive the Kerr solution in a pedagogically transparent way, using physical symmetry and gauge arguments to reduce the candidate metric to just two unknowns. The resulting field equations are then easy to obtain, and solve. Separately,…
Einstein equations with $T_{\mu\nu} = k_\mu k_\nu + \ell_\mu \ell_\nu$ where $k, \ell$ are null are considered with spherical symmetry and staticity. The solution has naked singularity and is not asymptotically flat. However, it may be…
The problem of comparison of the stationary axisymmetric vacuum solutions obtained within the framework of exact and approximate approaches for the description of the same general relativistic systems is considered. We suggest two ways of…
A class of stationary rigidly rotating perfect fluid coupled with non-linear electromagnetic fields was investigated. An exact solution of the Einstein equations with sources for the Carter B(+) branch was found, for the equation of state…
The general idea to modify Einstein's field equations by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$ was apparently outlined for the first time in [12-15]. The modification itself originates from…
A method is introduced for solving Einstein's equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the…
The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions.…
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…
The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order…
In this paper we show that any static and spherically symmetric anisotropic solution of the Einstein field equations can be thought as a system sourced by certain deformed isotropic system in the context of Minimal Geometric…
We treat the semiclassical Einstein equation as a quantum-classical hybrid and demonstrate the formal equivalence of its two derivation methods. This approach identifies the left-hand side of the equation as the expectation value of the…
We construct low regularity solutions of the vacuum Einstein constraint equations. In particular, on 3-manifolds we obtain solutions with metrics in $H^s\loc$ with $s>{3\over 2}$. The theory of maximal asymptotically Euclidean solutions of…
We discuss and prove an extended version of the Kerr theorem which allows one to construct exact solutions of the Einstein-Maxwell field equations from a holomorphic generating function $F$ of twistor variables. The exact multiparticle…
We study the affine quasi-Einstein Equation for homogeneous surfaces. This gives rise through the modified Riemannian extension to new half conformally flat generalized quasi-Einstein neutral signature $(2,2)$ manifolds, to conformally…