Related papers: Redshifts and Killing Vectors
We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We…
Starting with the most general four-dimensional spacetime possessing two commuting Killing vectors and a nontrivial Killing tensor, we analytically integrate Einstein-Yang-Mills equations for a completely arbitrary gauge group. It is…
Considered is the problem of local equivalence of generic four-dimensional metrics possessing two commuting and orthogonally transitive Killing vector fields. A sufficient set of eight differential invariants is explicitly constructed,…
We determine the asymptotic symmetry group of Killing horizons by choosing Gaussian null coordinates in the neighbourhood of the horizon and boundary conditions that respect the leading order terms in the metric. The analysis divides…
General relativity is reconsidered by starting from the unquestionable interpretation of special relativity, which (Klein 1910) is the theory of the invariants of the metric under the Poincar\'e group of collineations. This invariance…
The Newman-Penrose equations for spacetimes having one spacelike Killing vector are reduced -- in a geometrically defined "canonical frame'' -- to a minimal set, and its differential structure is studied. Expressions for the frame vectors…
It is shown that the metric of a massless particle obtained from boosting the Schwarzschild metric to the velocity of light, has four Killing vectors corresponding to an $E(2)\times \RR$ symmetry-group. This is in agreement with the…
In this paper, on basis of three quadratic differential operators leaving the form degree of an arbitrary differential form unchanged, that is, the d'Alembertian operator and two combined ones from the Hodge coderivative and the exterior…
Killing vector fields of a closed homogeneous and isotropic universe are studied. It is shown that in general case there is no time-like Killing vector fields in such a universe. Two exceptional cases are revealed.
A three-dimensional Riemannian manifold has locally 6, 4, 3, 2, 1 or none independent Killing vectors. We present an explicit algorithm for computing dimension of the infinitesimal isometry algebra. It branches according to the values of…
In principle, the local classification of spacetimes is always possible using the Cartan-Karlhede algorithm. However, in practice, the process of determining equivalence of two spacetimes is potentially computationally difficult or not at…
We study the existence of a non-spacelike isometry, \zeta, in higher dimensional Kundt spacetimes with constant scalar curvature invariants (CSI). We present the particular forms for the null or timelike Killing vectors and a set of…
Considering a spacetime foliated by co-dimension-2 hypersurfaces, we find the conditions under which lower-dimensional symmetries of a base space can be lifted up to irreducible Killing tensors of the full spacetime. In this construction,…
A new first integral for the equations corresponding to twisting type-N vacuum gravitational fields with two non-commuting Killing vectors is introduced. A new reduction of the problem to a complex second-order ordinary differential…
We generalize Killing equations to a test particle system which is subjected to external force. We relax the conservation condition by virtue of reparametrization invariance of a particle orbit. As a result, we obtain generalized Killing…
Many extensions of General Relativity are based on considering metric and affine structures as independent properties of spacetime. This leads to the possibility of introducing torsion as an independent degree of freedom. In this article we…
Main results concerning allowable additional symmetries of axially symmetric electrovacuum spacetimes are summarized. These are translational Killing vectors and the boost Killing vector. However, this is only the boost symmetry that does…
We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the…
In this paper we discuss the consequences of a Killing symmetry on the local geometrical structure of four-dimensional spacetimes. We have adopted the point of view introduced in recent works where the exterior derivative of the Killing…
We derive the equations corresponding to twisting type-N vacuum gravitational fields with one Killing vector and one homothetic Killing vector by using the same approach as that developed by one of us in order to treat the case with two…