349 citations · 2.2k across the 57 of their papers we have counts for
7 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…
Point Equivalence of Second-Order ODEs: Maximal Invariant Classification Order
Robert Milson, Francis Valiquette
We show that the local equivalence problem for second-order ordinary differential equations under point transformations is completely characterized by differential invariants of or…
Asymptotic behaviour of zeros of exceptional Jacobi and Laguerre polynomials
David Gómez-Ullate, Francisco Marcellán, Robert Milson
The location and asymptotic behaviour for large n of the zeros of exceptional Jacobi and Laguerre polynomials are discussed. The zeros of exceptional polynomials fall into two clas…
A conjecture on Exceptional Orthogonal Polynomials
David Gomez-Ullate, Niky Kamran, Robert Milson
Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and J…