1998/09/02 by Kevin Santosuosso, Denis Pollney, Nicos Pelavas +2
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Neuroimaging Techniques and Applications #Geometric Analysis and Curvature Flows #gr-qc #hep-th
paper · pdf · doi:10.1016/s0010-4655(98)00134-9
published as Comput.Phys.Commun. 115 (1998) 381-394 · 19 pages. To appear in Computer Physics Communications Thematic Issue on "Computer Algebra in Physics Research". Uses Maple2e.sty
arxiv created 1998/09/02 · openalex publication_date 1998/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use the computer algebra system GRTensorII to examine invariants polynomial in the Riemann tensor for class B warped product spacetimes - those which can be decomposed into the coupled product of two 2-dimensional spaces, one Lorentzian and one Riemannian, subject to the separability of the coupling: ds2 = dsΣ12 (u,v) + C(xγ)2 dsΣ22 (θ,ϕ) with C(xγ)2=r(u,v)2 w(θ,ϕ)2 and sig(Σ1)=0, sig(Σ2)=2ε(ε=± 1) for class B1 spacetimes and sig(Σ1)=2ε, sig(Σ2)=0 for class B2. Although very special, these spaces include many of interest, for example, all spherical, plane, and hyperbolic spacetimes. The first two Ricci invariants along with the Ricci scalar and the real component of the second Weyl invariant J alone are shown to constitute the largest independent set of invariants to degree five for this class. Explicit syzygies are given for other invariants up to this degree. It is argued that this set constitutes the largest functionally independent set to any degree for this class, and some physical consequences of the syzygies are explored.