===============================================================================
HELP FOR: PetrovReport
===============================================================================
CALLING SEQUENCE: PetrovReport():
-------------------------------------------------------------------------------
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.
-------------------------------------------------------------------------------
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).
-------------------------------------------------------
The quantities that could not be evaluated to zero are:
m
Weyl scalar Psi2 = - ----
3
r
-------------------------------------------------------------------------------
SEE ALSO: grt_basis, nptetrad, nprotate.
===============================================================================