Related papers: Redshifts and Killing Vectors
Fayos and Sopuerta have recently set up a formalism for studying vacuum spacetimes with an isometry, a formalism that is centred around the bivector corresponding to the Killing vector and that adapts the tetrad to the bivector. Steele has…
Asymptotically flat spacetimes with one Killing vector field are considered. The Killing equations are solved asymptotically using polyhomogeneous expansions (i.e. series in powers of 1/r an ln r), and solved order by order. The solution to…
We study vector fields generating a local flow by automorphisms of a parabolic geometry with higher order fixed points. We develop general tools extending the techniques of [1], [2], and [3]. We apply these tools to almost Grassmannian,…
In Class. Quantum Grav. 35 (2018) 155015 we have introduced the notion of "Multiple Killing Horizon" and analyzed some of its general properties. Multiple Killing Horizons are Killing horizons for two or more linearly independent Killing…
Continuous symmetries of spacetime such as spatial homogeneity and isotropy are rigorously defined using the concept of isometries and Killing vectors. In supergravity, the metric, or rather the tetrad, is not a standalone entity, but is…
In numerically constructing a spacetime that has an approximate timelike Killing vector, it is useful to choose spacetime coordinates adapted to the symmetry, so that the metric and matter variables vary only slowly with time in these…
We determine Killing vector fields on the $3$-dimensional space $\mathbb R^3$ endowed with a special diagonal metric.
We explore spacetime torsion in a two-dimensional setting, wherein it corresponds to a vector field. Without invoking field equations of a particular gravitational theory, we develop visualization techniques for such torsion fields,…
Given an d-dimensional manifold with two commuting Killing vectors, together with an d - 1 dimensional submanifold in which one of the Killing vectors lies, then the lapse and shift of the second Killing vector, relative to this slice,…
In a 5-dimensional spacetime ($M,g_{ab}$) with a Killing vector field $\xi ^a$ which is either everywhere timelike or everywhere spacelike, the collection of all trajectories of $\xi ^a$ gives a 4-dimensional space $S$. The reduction of…
In this text we combine the notions of supergeometry and supersymmetry. We construct a special class of supermanifolds whose reduced manifolds are (pseudo) Riemannian manifolds. These supermanifolds allow us to treat vector fields on the…
The solutions of generalized Killing equation have been obtained for line element with initial $t^2 \oplus so(3)$ symmetry. The coefficients of the metric $g$ corresponding to these vector fields are written down.
We study fixed points of isometries of the higher-dimensional Kerr-NUT-(A)dS spacetimes that form generalizations of symmetry axes. It turns out that, in the presence of nonzero NUT charges, some parts of the symmetry axes are necessarily…
The supersymmetry properties of Killing vectors and spinors in supergravity theory can be clarified by relating them to Killing supervectors in the supergravity superspace. In the superspace approach it is manifest that supersymmetry…
We consider an action that can generate fluids with three unequal stresses for metrics with a spacelike Killing vector. The parameters in the action are directly related to the stress anisotropies. The field equations following from the…
This paper presents a simple method for investigating spacetime symmetry for a given metric. The method makes use of the curvature conditions that are obtained from the Killing equations. We use the solutions of the curvature conditions to…
A new method is presented for finding Killing tensors in spacetimes with symmetries. The method is used to find all the Killing tensors of Melvin's magnetic universe and the Schwarzschild vacuum. We show that they are all trivial. The…
In these lectures the relations between symmetries, Lie algebras, Killing vectors and Noether's theorem are reviewed. A generalisation of the basic ideas to include velocity-dependend co-ordinate transformations naturally leads to the…
We devise an algorithm which allows one to count the number of Killing vectors for a Lorentzian manifold of dimension 3. Our algorithm relies on the principal traces of powers of the Ricci tensor and branches intricately according to the…
In the search for exact solutions to Einstein's field equations the main simplification tool is the introduction of spacetime symmetries. Motivated by this fact we develop a method to write the field equations for general matter in a form…