Related papers: Anholonomic Frames, Generalized Killing Equations,…
We solve the Einstein constraint equations for a 3 + 1 dimensional vacuum spacetime with a space-like translational Killing field in the asymptotically flat case.. The presence of a space-like translational Killing field allows for a…
This paper is the initial part of a comprehensive study of spacetimes that admit the canonical forms of Killing tensor in General Relativity. The general scope of the study is to derive either new exact solutions of Einstein's equations…
This work presents a novel methodology for deriving stationary and axially symmetric solutions to Einstein field equations using the 1+3 tetrad formalism. This approach reformulates the Einstein equations into first order scalar equations,…
In this paper we use the anholonomic frames method to construct exact solutions for vacuum 5D gravity with metrics having off-diagonal components. The solutions are in general anisotropic and possess interesting features such as an…
We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four and…
We consider exact solutions of Einstein equations defining static black holes parametrized by off-diagonal metrics which by anholonomic mappings can be equivalently transformed into some diagonal metrics with coefficients being very similar…
The generalized Killing equations and the symmetries of Taub-NUT spinning space are investigated. For spinless particles the Runge-Lenz vector defines a constant of motion directly, whereas for spinning particles it now requires a…
In this article we consider nonholonomic deformations of disk solutions in general relativity to generic off-diagonal metrics defining knew classes of exact solutions in 4D and 5D gravity. These solutions possess Lie algebroid symmetries…
We study stationary configurations mimicking nonholonomic locally anisotropic black rings (for instance, with ellipsoidal polarizations and/or imbedded into solitonic backgrounds) in three/six dimensional pseudo-Finsler/ Riemannian…
A new method of construction of integral varieties of Einstein equations in three dimensional (3D) and 4D gravity is presented whereby, under corresponding redefinition of physical values with respect to anholonomic frames of reference with…
The kinetic theory is formulated with respect to anholonomic frames of reference on curved spacetimes. By using the concept of nonlinear connection we develop an approach to modelling locally anisotropic kinetic processes and, in…
We apply the method of moving anholonomic frames, with associated nonlinear connections, in (pseudo) Riemannian spaces and examine the conditions when various types of locally anisotropic (la) structures (Lagrange, Finsler like and more…
We study new classes three dimensional black hole solutions of Einstein equations written in two holonomic and one anholonomic variables with respect to anholonomic frames Thermodynamic properties of such (2+1)-black holes with generic…
The gravitational equations of the three dimensional (3D) brane world are investigated for both off-diagonal and warped 5D metrics which can be diagonalized with respect to some anholonomic frames when the gravitational and matter fields…
The conditions for the existence of Killing-Yano tensors, which are closely related to the appearance of non-generic world-line SUSY, are presented for static axisymmetric spacetimes. Imposing the vacuum Einstein equation, the set of…
We synthesize and extend the previous ideas about appearance of both noncommutative and Finsler geometry in string theory with nonvanishing B--field and/or anholonomic (super) frame structures \cite{vstring,vstr2,vnonc,vncf}. There are…
We present a menagerie of solutions to the vacuum Einstein equations in six, eight and ten dimensions. These solutions describe spacetimes which are either locally asymptotically adS or locally asymptotically flat, and which have…
In this paper we examine a new class of five dimensional (5D) exact solutions in extra dimension gravity possessing Lie algebroid symmetry. The constructions provide a motivation for the theory of Clifford nonholonomic algebroids elaborated…
We establish a deformation framework for highly symmetric solutions to the Einstein equations. In this framework, four-dimensional metrics are constructed from three-dimensional {\eta}-Einstein metrics admitting a deformation determined by…
We show how one can systematically construct vacuum solutions to Einstein field equations with $D-2$ commuting Killing vectors in $D>4$ dimensions. The construction uses Einstein-scalar field seed solutions in 4 dimensions and is performed…