Related papers: Killing tensors in pp-wave spacetimes
Conformal Killing equations and their integrability conditions for nonexpanding hyperheavenly spaces with Lambda are studied. Reduction of ten Killing equations to one master equation is presented. Classification of homothetic and isometric…
The use of Lax pair tensors as a unifying framework for Killing tensors of arbitrary rank is discussed. Some properties of the tensorial Lax pair formulation are stated. A mechanical system with a well-known Lax representation -- the…
The Killing tensors of arbitrary rank on complex projective space with its Fubini-Study metric are determined and it is shown that these spaces are generated by the Killing fields.
The integrability conditions for the existence of Killing-Yano tensors or, equivalently, covariantly closed conformal Killing-Yano tensors, in the presence of torsion are worked out. As an application, all metrics and torsions compatible…
We employ the G-structure formalism to study supersymmetric solutions of minimal and SU(2) gauged supergravities in seven dimensions admitting Killing spinors with associated timelike Killing vector. The most general such Killing spinor…
The Killing spinor equations for pp-wave solutions of eleven dimensional supergravity are analysed and it is shown that there are solutions that preserve 18,20,22 and 24 supersymmetries, in addition to the generic solution preserving 16…
In this paper the isometries of the dual space were investigated. The dual structural equations of a Killing tensor of order two were found . The flat space case was analyzed in details.
Some basic theorems on Killing vector fields are reviewed. In particular, the topic of a constant-curvature space is examined. A detailed proof is given for a theorem describing the most general form of the metric of a homogeneous isotropic…
We study Killing tensors in the context of warped products and apply the results to the problem of orthogonal separation of the Hamilton-Jacobi equation. This work is motivated primarily by the case of spaces of constant curvature where…
A symmetric tensor field on a Riemannian manifold is called Killing field if the symmetric part of its covariant derivative is equal to zero. There is a one to one correspondence between Killing tensor fields and first integrals of the…
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…
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…
A definition is suggested for affine symmetry tensors, which generalize the notion of affine vectors in the same way that (conformal) Killing tensors generalize (conformal) Killing vectors. An identity for these tensors is proved, which…
The Killing tensor equation is a first order differential equation on symmetric covariant tensors that generalises to higher rank the usual Killing vector equation on Riemannian manifolds. We view this more generally as an equation on any…
Algebraic curvature tensors possess generators which can be formed from symmetric or alternating tensors S, A or tensors \theta with an irreducible (2,1)-symmetry. In differential geometry examples of curvature formulas are known which…
We study Killing vector fields in asymptotically flat space-times. We prove the following result, implicitly assumed in the uniqueness theory of stationary black holes. If the conditions of the rigidity part of the positive energy theorem…
In this paper, we investigate spacetime characterized by a hidden symmetry defined by a given Killing tensor. To exhibit this hidden symmetry, the inverse metric must commute with the Killing tensor under the Schouten-Nijenhuis bracket,…
Anti-self-dual (ASD) 4-dimensional complex Einstein spaces with nonzero cosmological constant $\Lambda$ equipped with a nonnul Killing vector are considered. It is shown, that any conformally nonflat metric of such spaces can be always…
Recently, the authors have formulated and explored a novel Painleve-Gullstrand variant of the Lense-Thirring spacetime, which has some particularly elegant features -- including unit-lapse, intrinsically flat spatial 3-slices, and some…
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…