349 citations · 2.2k across the 57 of their papers we have counts for
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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…
Supersymmetry and algebraic deformations
D. Gomez-Ullate, N. Kamran, R. Milson
We describe a class of algebraically solvable SUSY models by considering the deformation of invariant polynomial flags by means of the Darboux transformation. The algebraic deforma…
Quasi-Exact Solvability and the direct approach to invariant subspaces
D. Gomez-Ullate, N. Kamran, R. Milson
We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of…
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…