• A spacetime not characterized by its invariants is of aligned type II 

      Hervik, Sigbjørn (Journal article; Peer reviewed, 2011)
      By using invariant theory we show that a (higher-dimensional) Lorentzian metric that is not characterised by its invariants must be of aligned type II; i.e., there exists a frame such that all the curvature tensors ...
    • All metrics have curvature tensors characterised by its invariants as a limit: the ϵ-property 

      Hervik, Sigbjørn (Journal article; Peer reviewed, 2011)
      We prove a generalisation of the ϵ-property, namely that for any dimension and signature, a metric which is not characterised by its polynomial scalar curvature invariants, there is a frame such that the components of the ...
    • 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 ...
    • Inflation with stable anisotropic hair 

      Hervik, Sigbjørn; Mota, David F.; Thorsrud, Mikjel (Journal article; Peer reviewed, 2011)
      Recently an inflationary model with a vector field coupled to the inflaton was proposed and the phenomenology studied for the Bianchi type I spacetime. It was found that the model demonstrates a counter-example to the ...
    • A mathematical approach to Wick rotations 

      Helleland, Christer (PhD thesis UiS;536, Doctoral thesis, 2020-09)
      In this thesis we define Wick-rotations mathematically using pseudo-Riemannian geometry, and relate Wick-rotations to real geometric invariant theory (GIT). We discover some new results concerning the existence of Wick ...
    • Nil-Killing vector fields and Kundt structures 

      Aadne, Matthew Terje (PhD thesis UiS;529, Doctoral thesis, 2020-06)
      This thesis is based on three papers, for which two have been submitted for publication and one is published. A chapter presenting relevant background material is included giving convenient access to preliminary foreknowledge ...
    • 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 ...
    • Pseudo-Riemannian VSI spaces II 

      Hervik, Sigbjørn (Journal article; Peer reviewed, 2012)
      In this paper we consider pseudo-Riemannian spaces of arbitrary signature for which all of the polynomial curvature invariants vanish (VSI spaces). Using an algebraic classification of pseudo-Riemannian spaces in terms of ...
    • Ricci nilsoliton black holes 

      Hervik, Sigbjørn (Journal article; Peer reviewed, 2008)
      We follow a constructive approach and find higher-dimensional black holes with Ricci nilsoliton horizons. The spacetimes are solutions to the Einstein equation with a negative cosmological constant and generalise therefore, ...
    • Tales from Wonderland 

      Normann, Ben David (Doctoral thesis, 2020-06)
      Knowing that the Universe is quite isotropic, one may, as already discussed in Chapter 1, wonder how likely such a Universe is. We take the following research question. Question 1. Is the asymptotic future of a cosmology ...
    • Type III and II universal spacetimes 

      Hervik, Sigbjørn; Pravdova, Alena; Pravda, Vojtech (Journal article; Peer reviewed, 2015)
      We briefly summarize our recent results on universal spacetimes. We show that universal spacetimes are necessarily CSI, i.e. for these spacetimes, all curvature invariants constructed from the Riemann tensor and its ...
    • Type N universal spacetimes 

      Hervik, Sigbjørn; Pravda, V; Pravdova, A (Journal article; Peer reviewed, 2015)
      Universal spacetimes are vacuum solutions to all theories of gravity with the Lagrangian L [...]. Well known examples of universal spacetimes are plane waves which are of the Weyl type N. Here, we discuss recent results ...
    • Universal Black Holes 

      Hervik, Sigbjørn; Ortaggio, Marcello (Peer reviewed; Journal article, 2020-02)
      We prove that a generalized Schwarzschild-like ansatz can be consistently employed to construct d-dimensional static vacuum black hole solutions in any metric theory of gravity for which the Lagrangian is a scalar invariant ...
    • Universal spacetimes in four dimensions 

      Hervik, Sigbjørn; Pravda, Vojtech; Pravdova, Alena (Journal article; Peer reviewed, 2017-10)
      Universal spacetimes are exact solutions to all higher-order theories of gravity. We study these spacetimes in four dimensions and provide necessary and sufficient conditions for universality for all Petrov types except ...