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HELP FOR: PetrovReport
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CALLING SEQUENCE:  PetrovReport():

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SYNOPSIS:

- Generates a report detailing how the determination of the Petrov type
  of a spacetime was carried out.

- The object Petrov (calculated for null tetrads using grcalc) is determined
  using an algorithm detailed in

  Letniowski, F. W., and McLenaghan, R. G., 1988, Gen. Rel. Grav., 20,
    463-83.

  The notation of this paper is used by PetrovReport() in referring to
  intermediate variables.

  The success of the algorithm depends on determining whether certain 
  functions of the Weyl scalars can be evaluated to zero. It is sometimes
  the case that the computer can not simplify an expression which, upon
  inspection, is clearly equal to zero. In these rare cases, the Petrov
  algorithm will fail in that it will report a Petrov type which is more
  complex than the true value. Using the report command, the intermediate
  steps taken in determination of the Petrov type can be examined and
  evaluated for correctness.

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EXAMPLES:

> qload ( schw ):

                              Default metric = schw

                                   Coordinates

                              For the schw metric.

                      1        2            3          4
                    x   = r, x   = theta, x   = phi, x   = t

                                  Line element

                              For the schw metric.

    2
  ds  =

           2
        d r       2         2     2           2       2                      2
     --------- + r   d theta   + r  sin(theta)   d phi   + (- 1 + 2 m/r)  d t
     1 - 2 m/r

> nptetrad ( [ 0, 0, 0, 1 ] ):

Calculated detg for schw. (0.017000 sec.) 
Calculated g(up,up) for schw. (0.100000 sec.) 

The null tetrad has been stored as e(bdn,up).

> grcalc ( WeylSc ):

> grdisplay ( WeylSc ):

                              For the schw metric.

                                Weyl Scalar, Psi0

                                    Psi0 = 0

                                Weyl Scalar, Psi1

                                    Psi1 = 0

                                  Scalar, Psi2

                                             m
                                   Psi2 = - ----
                                              3
                                             r

                                Weyl Scalar, Psi3

                                    Psi3 = 0

                                Weyl Scalar, Psi4

                                    Psi4 = 0

> grcalc ( Petrov ):

> grdisplay ( Petrov ):

                              For the schw metric.

                                   Petrov Type

                          Petrov Type  = D (or simpler)

> PetrovReport ():

                  The conclusion 'Petrov type = D (or simpler)'

                               for the schw metric

                       was based on the following results:

                              Weyl scalar Psi0 = 0

                              Weyl scalar Psi1 = 0

                Weyl scalar Psi2 could not be evaluated to zero.

                              Weyl scalar Psi3 = 0

                              Weyl scalar Psi4 = 0

               ---> Therefore the metric is Petrov D (or simpler).

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            The quantities that could not be evaluated to zero are:

                                                   m
                             Weyl scalar Psi2 = - ----
                                                    3
                                                   r

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SEE ALSO: grt_basis, nptetrad, nprotate.
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