• Comment on ''Szekeres universes with homogeneous scalar fields'' 

      Delgado Gaspar, Ismael; Sussman, Roberto A.; McNutt, David Duncan; Coley, Alan (Peer reviewed; Journal article, 2021-04)
      In two recently published articles, Barrow and Paliathanasis (2018, 2019) [1, 2] claim to have found exact solutions of Einstein’s field equations belonging to the class of non-trivial (i.e., spatially inhomogeneous) ...
    • Curvature operators and scalar curvature invariants 

      Hervik, Sigbjørn; Coley, Alan (Journal article; Peer reviewed, 2010)
      We continue the study of the question of when a pseudo-Riemannain manifold can be locally characterised by its scalar polynomial curvature invariants (constructed from the Riemann tensor and its covariant deriva- tives). ...
    • Discriminating the Weyl type in higher dimensions using scalar curvature invariants 

      Hervik, Sigbjørn; Coley, Alan (Journal article; Peer reviewed, 2011)
      We consider higher dimensional Lorentzian spacetimes which are currently of interest in theoretical physics. It is possible to algebraically classify any tensor in a Lorentzian spacetime of arbitrary dimensions using ...
    • Higher dimensional bivectors and classification of the Weyl operator 

      Hervik, Sigbjørn; Coley, Alan (Journal article; Peer reviewed, 2010)
      We develop the bivector formalism in higher dimensional Lorentzian spacetimes. We define the Weyl bivector operator in a manner consis- tent with its boost-weight decomposition. We then algebraically classify the Weyl ...
    • Invariant characterization of Szekeres models with positive cosmological constant 

      McNutt, David Duncan; Coley, Alan; Layden, Nicolas (Peer reviewed; Journal article, 2022-07)
      We present an invariant characterization of black holes in the Szekeres spacetime with positive cosmological constant. In the formation of the black holes, we locate geometric horizons, and show that they coincide with the ...
    • Note on the invariant classification of vacuum type D spacetimes 

      Coley, Alan; Hervik, Sigbjørn (Journal article; Peer reviewed, 2009-12)
      We illustrate the fact that the class of vacuum type D spacetimes which are I-non-degenerate are invariantly classified by their scalar polynomial curvature invariants.
    • On the algebraic classification of pseudo-Riemannian spaces 

      Hervik, Sigbjørn; Coley, Alan (Journal article; Peer reviewed, 2011-12)
      We consider arbitrary-dimensional pseudo-Riemannian spaces of signature (k, k + m). We introduce a boost-weight decomposition and define a number of algebraic properties (e.g. the Si- and N-properties) and present a ...
    • Pseudo-Riemannian VSI spaces 

      Hervik, Sigbjørn; Coley, Alan (Journal article; Peer reviewed, 2011)
      In this paper we consider pseudo-Riemannian spaces of arbitrary sig- nature for which all of their polynomial curvature invariants vanish (VSI spaces). We discuss an algebraic classification of pseudo-Riemannian spaces ...
    • Symmetric teleparallel geometries 

      Coley, Alan; van den Hoogen, Robert; McNutt, David Duncan (Peer reviewed; Journal article, 2022)
      In teleparallel gravity and, in particular, in F(T) teleparallel gravity, there is a challenge in determining an appropriate (co-)frame and its corresponding spin connection to describe the geometry. Very often, the ‘proper’ ...
    • Symmetry and Equivalence in Teleparallel Gravity 

      Coley, Alan; van den Hoogen, Robert; McNutt, David Duncan (Peer reviewed; Journal article, 2020-07)
      In theories such as teleparallel gravity and its extensions, the frame basis replaces the metric tensor as the primary object of study. A choice of coordinate system, frame basis, and spin-connection must be made to obtain ...