permutations SciMax Toolbox pfeformat

SciMax Toolbox >> petrov

petrov

Maxima Function

Calling Sequence

petrov ()

Description

Computes the Petrov classification of the metric characterized by psi[0]...psi[4].

For example, the following demonstrates how to obtain the Petrov-classification of the Kerr metric:

(%i1) load(ctensor);
(%o1)       /share/tensor/ctensor.mac
(%i2) (cframe_flag:true,gcd:spmod,ctrgsimp:true,ratfac:true);
(%o2)                                true
(%i3) ct_coordsys(exteriorschwarzschild,all);
(%o3)                                done
(%i4) ug:invert(lg)$
(%i5) weyl(false);
(%o5)                                done
(%i6) nptetrad(true);
(%t6) np =
[ sqrt(r - 2 m)           sqrt(r)                                 ]
[---------------   ---------------------    0            0        ]
[sqrt(2) sqrt(r)   sqrt(2) sqrt(r - 2 m)                          ]
[                                                                 ]
[ sqrt(r - 2 m)            sqrt(r)                                ]
[---------------  - ---------------------   0            0        ]
[sqrt(2) sqrt(r)    sqrt(2) sqrt(r - 2 m)                         ]
[                                                                 ]
[                                          r      %i r sin(theta) ]
[       0                    0          -------   --------------- ]
[                                       sqrt(2)       sqrt(2)     ]
[                                                                 ]
[                                          r       %i r sin(theta)]
[       0                    0          -------  - ---------------]
[                                       sqrt(2)        sqrt(2)    ]
                             sqrt(r)         sqrt(r - 2 m)
(%t7) npi = matrix([- ---------------------,---------------, 0, 0],
                      sqrt(2) sqrt(r - 2 m) sqrt(2) sqrt(r)
          sqrt(r)            sqrt(r - 2 m)
[- ---------------------, - ---------------, 0, 0],
   sqrt(2) sqrt(r - 2 m)    sqrt(2) sqrt(r)
           1               %i
[0, 0, ---------, --------------------],
       sqrt(2) r  sqrt(2) r sin(theta)
           1                 %i
[0, 0, ---------, - --------------------])
       sqrt(2) r    sqrt(2) r sin(theta)
(%o7)                                done
(%i7) psi(true);
(%t8)                              psi  = 0
                                      0
(%t9)                              psi  = 0
                                      1
                                          m
(%t10)                             psi  = --
                                      2    3
                                          r
(%t11)                             psi  = 0
                                      3
(%t12)                             psi  = 0
                                      4
(%o12)                               done
(%i12) petrov();
(%o12)                                 D

The Petrov classification function is based on the algorithm published in "Classifying geometries in general relativity: III Classification in practice" by Pollney, Skea, and d'Inverno, Class. Quant. Grav. 17 2885-2902 (2000). Except for some simple test cases, the implementation is untested as of December 19, 2004, and is likely to contain errors.

permutations SciMax Toolbox pfeformat