Faculty of Mathematical Studies

University of Southampton
United Kingdom

Symbolic Computation Group
Dept of Theoretical Physics

Instituto de Física

Welcome To The On-Line Invariant Classification Database.

First-time users should probably access the How To Use The Database page first. Note the new keyword and Exact Solutions searches added at the bottom of this page.

Petrov Type

Petrov Type I II III D N O

Segre Type

Segre Type 0 [1,(111)] [(1,1)(11)] [(211)] [(1,1)11] [1,1(11)] [(1,11)1]
Notes vacuum perfect fluid includes non-null e.-m. radiation null fluid boost isotropy rotational isotropy tachyon fluid
Segre Type [(21)1] [2(11)] [211] [31] [(31)] [1,111] [zz11] [zz(11)]
Notes null isotropy [2(11)] Plebanski Petrov II Plebanski Petrov III 4 null directions coincide general real general complex fails energy conditions

Trace of Ricci Tensor

Zero Non-Zero

Maximal Isometry Group

Dimension 0 1 2 3 4 5 6 7 10

Maximal Isotropy Subgroup

Isotropy Group 0 Boost Spatial Rots. 1-D Null Rots. Boost+ Spatial Rots. 2-D Null Rots. SO(3) SO(2,1) Null + Spatial Rots. Full Lorentz Group
Dimension 0 1 1 1 2 2 3 3 3 6

Number of Essential Coordinates

Coordinates 0 (Homogeneous) 1 2 3 4

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Search for a metric in Kramer et al.

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Author: Jim Skea, of the Symbolic Computation Group of the Department of Theoretical Physics at UERJ (Universidade do Estado de Rio de Janeiro).
Jim Skea gratefully acknowledges the support of the Fundação de Amparo de Pesquisas do Estado do Rio de Janeiro (FAPERJ).

Last modified 18-12-96
Mail comments to rdi@maths.soton.ac.uk. jimsk@symbcomp.uerj.br.