Related papers: Redshifts and Killing Vectors
We provide a general method for studying a manifestly covariant formulation of $p$-form gauge theories on the de Sitter space. This is done by stereographically projecting the corresponding theories, defined on flat Minkowski space, onto…
New similarity variables are introduced for the Einstein - Maxwell equations with one Killing vector that reduce the non-linear partial differential equations in three independent variables to ordinary differential equations. These…
A characterization of the Kerr-NUT-(A)de Sitter metric among four dimensional \Lambda-vacuum spacetimes admitting a Killing vector is obtained in terms of the proportionality of the self-dual Weyl tensor and a natural self-dual double…
This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity…
Let $M$ be a locally rotationally symmetric spacetime, and $\xi^a$ a conformal Killing vector for the metric on $M$, lying in the subspace spanned by the unit timelike direction and the preferred spatial direction, and with non-constant…
We study Finsler spacetimes and Killing vector fields taking care of the fact that the generalized metric tensor associated to the Lorentz-Finsler function $L$ is in general well defined only on a subset of the slit tangent bundle. We then…
This paper locally classifies finite-dimensional Lie algebras of conformal and Killing vector fields on $\mathbb{R}^2$ relative to an arbitrary pseudo-Riemannian metric. Several results about their geometric properties are detailed, e.g.…
Vector fields are a highly abstract physical concept that is often taught using visualizations. Although vector representations are particularly suitable for visualizing quantitative data, they are often confusing, especially when…
The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most…
The Separation of Variables theory for the Hamilton-Jacobi equation is 'by definition' related to the use of special kinds of coordinates, for example Jacobi coordinates on the ellipsoid or St\"ackel systems in the Euclidean space. However,…
There are a wide variety of different vector formalisms currently utilized in engineering and physics. For example, Gibbs' three-vectors, Minkowski four-vectors, complex spinors in quantum mechanics, quaternions used to describe rigid body…
In this paper, we study generalized $m$-quasi-Einstein $(M^n,g,X,\lambda)$ under natural conditions on the potential vector field. We show that, under suitable integral assumptions, the potential vector field is Killing, extending earlier…
The confrontation between general relativity (and its theoretically most plausible deviations) and experimental or observational results is summarized. Some discussion is devoted to the various methodologies used in confronting theory and…
In the extremal Kerr spacetime the horizon Killing vector field is null on a timelike hypersurface crossing the horizon at a fixed latitude, and spacelike on both sides of the horizon in the equatorial plane. We explain in some detail how…
Gowdy spacetimes are generalized to admit two commuting spatial "local" Killing vectors, and some new varieties of them are presented, which are all closely related to Thurston's geometries. Explicit spatial compactifications, as well as…
A Theorem is proved which reduces the problem of completeness of orbits of Killing vector fields in maximal globally hyperbolic, say vacuum, space--times to some properties of the orbits near the Cauchy surface. In particular it is shown…
We study the influence of the instantaneous appearance of a conformal Killing vector (CKV) in self-gravitating fluid spheres during their evolution. For doing that we introduce a tensor variable whose time dependence allows the existence of…
In this paper we consider homothetic Killing vectors in the class of stationary axisymmetric vacuum (SAV) spacetimes, where the components of the vectors are functions of the time and radial coordinates. In this case the component of any…
The 14 Killing vectors of the target space for five-dimensional minimal supergravity reduced to three dimensions are explicitly constructed in terms of the original field variables. These vectors generate the Lie algebra of $G_2$. We also…
This note describes a local scheme to characterize and normalize an axial Killing field on a general Riemannian geometry. No global assumptions are necessary, such as that the orbits of the Killing field all have period $2 \pi$. Rather, any…