Related papers: Conformal motions in plane symmetric static spacet…
The most general set of static and spherically symmetric solutions for conformal Killing gravity coupled to Maxwell fields is presented in closed form. These solutions, depending on six parameters, include non-asymptotically flat black…
Using Lie symmetry methods for differential equations we have investigated the symmetries of a Lagrangian for a plane symmetric static spacetime. Perturbing this Lagrangian we explore its approximate symmetries. It has a non-trivial…
We consider plane symmetric gravitational fields within the framework of General Relativity in (D+1)-dimensional spacetime. Two classes of vacuum solutions correspond to higher-dimensional generalizations of the Rindler and Taub spacetimes.…
The infinite cosmological "constant" limit of the de Sitter solutions to Einstein's equation is studied. The corresponding spacetime is a singular, four-dimensional cone-space, transitive under proper conformal transformations, which…
The main intention of the paper is to investigate an osculating curve under the conformal map. We obtain a sufficient condition for the conformal invariance of an osculating curve. We also find an equivalent system of a geodesic curve under…
Symmetries concerning the ordinary coordinate spacetime and internal spacetime are discussed. A possible unification model of electroweak, strong and gravitational interactions is briefly described.
In this article on the basis of a new definition of spacetime symmetry, which is in accordance with the symmetry of the curvature invariants, we investigate exact vacuum solutions of Einstein field equations corresponding to both static and…
The Hamiltonian structure of spacetimes with two commuting Killing vector fields is analyzed for the purpose of addressing the various problems of time that arise in canonical gravity. Two specific models are considered: (i) cylindrically…
We start a systematic investigation of possible isometries of the asymptotically de Sitter solutions to Einstein equations. We reformulate the Killing equation as conformal equations for the initial data at $\mathcal{I}^+$. This allows for…
The conformal Killing equations for the most general (non-plane wave) conformally flat pure radiation field are solved to find the conformal Killing vectors. As expected fifteen independent conformal Killing vectors exist, but in general…
A study of conformally flat but non flat Bianchi type I and cylindrically symmetric static space-times according to proper projective symmetry is given by using some algebraic and direct integration techniques. It is shown that the special…
Self-similar spacetimes are of importance to cosmology and to gravitational collapse problems. We show that self-similarity or the existence of a homothetic Killing vector field for spherically symmetric spacetimes implies the separability…
The present study deals with the inhomogeneous plane symmetric models in scalar - tensor theory of gravitation. We used symmetry group analysis method to solve the field equations analytically. A new class of similarity solutions have been…
Spherically symmetric solutions admitting a homothetic Killing vector field (HKVF) either orthogonal, $\eta_{\bot}$, or parallel,$\eta_{||}$, to the 4-velocity vector field, $u^a$, are studied. New self-similar solution of Einstein's field…
Conformal Killing equations and their integrability conditions for expanding hyperheavenly spaces with Lambda in spinorial formalism are studied. It is shown that any conformal Killing vector reduces to homothetic or isometric Killing…
A class of exact conformastatic solutions of the Einstein-Maxwell field equations is presented in which the gravitational and electromagnetic potentials are completely determined by a harmonic function only. The motion of test particles is…
Conformally compactified phase space is conceived as an automorphism space for the global action of the extended conformal group. Space time and momentum space appear then as conformally dual, that is conjugate with respect to conformal…
A class of exact solutions of the gravitational field equations in the vacuum on the brane are obtained by assuming the existence of a conformal Killing vector field, with non-static and non-central symmetry. In this case the general…
This paper discusses some of the physical properties of plane symmetric self-similar solutions of the first kind (i.e., homothetic solutions). We are interested in calculating the expansion, the acceleration, the rotation, the shear tensor,…
We study the conformal Killing equation for generic Vaidya-like spacetimes, including those with rotation. We show that these spacetimes admit a unique class of conformal Killing vectors that are homothetic for mass, charge, or rotation…