349 citations · 2.2k across the 57 of their papers we have counts for
13 papers · 1 filter
Vacuum Plane Waves; Cartan Invariants and physical interpretation
Alan Coley, David McNutt, Robert Milson
As an application of the Cartan invariants obtained using the Karlhede algorithm, we study a simple subclass of the PP-wave spacetimes, the gravitational plane waves. We provide an…
Three-dimensional spacetimes of maximal order
Robert Milson, Lode Wylleman
We show that the equivalence problem for three-dimensional Lorentzian manifolds requires at most the fifth covariant derivative of the curvature tensor. We prove that this bound is…
Invariant classification of vacuum PP-waves
Robert Milson, David McNutt, Alan Coley
We solve the equivalence problem for vacuum PP-wave spacetimes by employing the Karlhede algorithm. Our main result is a suite of Cartan invariants that allows for the complete inv…
Vacuum Kundt Waves
David McNutt, Robert Milson, Alan Coley
We discuss the invariant classification of vacuum Kundt waves using the Cartan-Karlhede algorithm, and the upper bound on the number of iterations of the Karlhede algorithm to clas…
The curvature homogeneity bound for Lorentzian four-manifolds
Robert Milson, Nicos Pelavas
We prove that a four-dimensional Lorentzian manifold that is curvature homogeneous of order 3, or CH_3 for short, is necessarily locally homogeneous. We also exhibit and classify f…
The type N Karlhede bound is sharp
Robert Milson, Nicos Pelavas
We present a family of four-dimensional Lorentzian manifolds whose invariant classification requires the seventh covariant derivative of the curvature tensor. The spacetimes in que…
On curvature homogeneous 4D Lorentzian manifolds
R. Milson, N. Pelavas
We prove that a four-dimensional Lorentzian manifold that is curvature homogeneous of order 3, or $\CH_3$ for short, is necessarily locally homogeneous. We also exhibit and classif…
Vanishing Scalar Invariant Spacetimes in Higher Dimensions
A. Coley, R. Milson, V. Pravda +1
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 e…
Alignment and the classification of Lorentz-signature tensors
Robert Milson
We define the notion of an aligned null direction, a Lorentz-signature analogue of the eigenvector concept that is valid for arbitrary tensor types. The set of aligned null directi…
Classification of the Weyl Tensor in Higher Dimensions
A. Coley, R. Milson, V. Pravda +1
We discuss the algebraic classification of the Weyl tensor in higher dimensional Lorentzian manifolds. This is done by characterizing algebraically special Weyl tensors by means of…
Bianchi identities in higher dimensions
V. Pravda, A. Pravdova, A. Coley +1
A higher dimensional frame formalism is developed in order to study implications of the Bianchi identities for the Weyl tensor in vacuum spacetimes of the algebraic types III and N…
Alignment and algebraically special tensors in Lorentzian geometry
R. Milson, A. Coley, V. Pravda +1
We develop a dimension-independent theory of alignment in Lorentzian geometry, and apply it to the tensor classification problem for the Weyl and Ricci tensors. First, we show that…
All spacetimes with vanishing curvature invariants
V. Pravda, A. Pravdova, A. Coley +1
All Lorentzian spacetimes with vanishing invariants constructed from the Riemann tensor and its covariant derivatives are determined. A subclass of the Kundt spacetimes results and…