ISOMETRIES IN HIGHER-DIMENSIONAL CCNV SPACETIMES (original) (raw)

CCNV Spacetimes and (Super)symmetries

It is of interest to study supergravity solutions preserving a non-minimal fraction of supersymmetries. A necessary condition for supersymmetry to be preserved is that the spacetime admits a Killing spinor and hence a null or timelike Killing vector. Spacetimes admitting a covariantly constant null vector (CCNV), and hence a null Killing vector, belong to the Kundt class. We investigate the existence of additional isometries in the class of higher-dimensional CCNV Kundt metrics.

General approach to the study of vacuum spacetimes with an isometry

Classical and Quantum Gravity, 2001

In vacuum space-times the exterior derivative of a Killing vector field is a 2-form (named here as the Papapetrou field) that satisfies Maxwell's equations without electromagnetic sources. In this paper, using the algebraic structure of the Papapetrou field, we will set up a new formalism for the study of vacuum spacetimes with an isometry, which is suitable to investigate the connections between the isometry and the Petrov type of the space-time. This approach has some advantages, among them, it leads to a new classification of these space-times and the integrability conditions provide expressions that determine completely the Weyl curvature. These facts make the formalism useful for application to any problem or situation with an isometry and requiring the knowledge of the curvature.

Kundt spacetimes

Classical and Quantum Gravity, 2009

Kundt spacetimes are of great importance in general relativity in four dimensions and have a number of physical applications in higher dimensions in the context of string theory. The degenerate Kundt spacetimes have many special and unique mathematical properties, including their invariant curvature structure and their holonomy structure. We provide a rigorous geometrical kinematical definition of the general Kundt spacetime in four dimensions; essentially a Kundt spacetime is defined as one admitting a null vector that is geodesic, expansion-free, shear-free and twist-free. A Kundt spacetime is said to be degenerate if the preferred kinematic and curvature null frames are all aligned. The degenerate Kundt spacetimes are the only spacetimes in four dimensions that are not I-non-degenerate, so that they are not determined by their scalar polynomial curvature invariants. We first discuss the non-aligned Kundt spacetimes, and then turn our attention to the degenerate Kundt spacetimes. The degenerate Kundt spacetimes are classified algebraically by the Riemann tensor and its covariant derivatives in the aligned kinematic frame; as an example, we classify Riemann type D degenerate Kundt spacetimes in which ∇(Riem), ∇ (2) (Riem) are also of type D. We discuss other local characteristics of the degenerate Kundt spacetimes. Finally, we discuss degenerate Kundt spacetimes in higher dimensions.

Noether Symmetries Versus Killing Vectors and Isometries of Spacetimes

International Journal of Theoretical Physics, 2006

Symmetries of spacetime manifolds which are given by Killing vectors are compared with the symmetries of the Lagrangians of the respective spacetimes. We find the point generators of the one parameter Lie groups of transformations that leave invariant the action integral corresponding to the Lagrangian (Noether symmetries). In the examples considered, it is shown that the Noether symmetries obtained by considering the Larangians provide additional symmetries which are not provided by the Killing vectors. It is conjectured that these symmetries would always provide a larger Lie algebra of which the KV symmetres will form a subalgebra.

Vanishing scalar invariant spacetimes in higher dimensions

Classical and Quantum Gravity, 2004

We study manifolds with Lorentzian signature and prove that all scalar curvature invariants of all orders vanish in a higher dimensional Lorentzian spacetime if and only if there exists an aligned non-expanding, non-twisting, geodesic null direction along which the Riemann tensor has negative boost order.

Axially Symmetric, Spatially Homothetic Spacetimes

We show that the existence of appropriate spatial homothetic Killing vectors is directly related to the separability of the metric functions for axially symmetric spacetimes. The density profile for such spacetimes is (spatially) arbitrary and admits any equation of state for the matter in the spacetime. When used for studying axisymmetric gravitational collapse, such solutions do not result in a locally naked singularity.

Killing Symmetries of Generalized Minkowski Spaces, 3: Spacetime Translations in Four Dimensions

Foundations of Physics, 2000

In this paper, we continue the study of the Killing symmetries of a N-dimensional generalized Minkowski space, i.e. a space endowed with a (in general non-diagonal) metric tensor, whose coefficients do depend on a set of non-metrical coordinates. We discuss here the finite structure of the space-time rotations in such spaces, by confining ourselves (without loss of generality) to the four-dimensional 1 case. In particular, the results obtained are specialized to the case of a "deformed" Minkowski space M 4 (i.e. a pseudoeuclidean space with metric coefficients depending on energy), for which we derive the explicit general form of the finite rotations and boosts in different parametric bases.

On spacetimes with given kinematical invariants: construction and examples

2010

We present a useful method for the construction of cosmological models by solving the differential equations arising from calculating the kinematical invariants (shear, rotation, expansion and acceleration) of an observer field in proper time description. As an application of our method we present two generalizations of the Gödel spacetime that follow naturally from our approach.

A note on Noether symmetries and conformal Killing vectors

General Relativity and Gravitation, 2010

A conjecture was stated in Hussain et al. (Gen Relativ Grav 41:2399, that the conformal Killing vectors form a subalgebra of the symmetries of the Lagrangian that minimizes arc length, for any spacetime. Here, a counter example is constructed to demonstrate that the above statement is not true in general for spacetimes of non-zero curvature.

Constructing the CKVs of Bianchi III and V spacetimes

Modern Physics Letters A, 2019

We determine the conformal algebra of Bianchi III and Bianchi V spacetimes or, equivalently, we determine all Bianchi III and Bianchi V spacetimes which admit a proper conformal Killing vector (CKV). The algorithm that we use has been developed in [M. Tsamparlis et al.Class. Quantum. Grav. 15, 2909 (1998)] and concerns the computation of the CKVs of decomposable spacetimes. The main point of this method is that a decomposable space admits a CKV if the reduced space admits a gradient homothetic vector, the latter being possible only if the reduced space is flat or a space of constant curvature. We apply this method in a stepwise manner starting from the two-dimensional spacetime which admits an infinite number of CKVs and we construct step by step the Bianchi III and V spacetimes by assuming that CKVs survive as we increase the dimension of the space. We find that there is only one Bianchi III and one Bianchi V spacetime which admit at maximum one proper CKV. In each case, we determi...