(*^

::[	frontEndVersion = "Microsoft Windows Mathematica Notebook Front End Version 2.2";
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Mma2 95 statlim

:[font = input; startGroup; nowordwrap; ]
<<grii/grt.m
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No Input Form Generated

;[o]
 GRTensorM Version 1.0
 June 4, 1996
 Copyright 1996 by P. Musgrave, D. Pollney and K. Lake
 Use qload[] or grload[] to load a metric.
 ?grtensor for help.
 Metric directory = "c:/wnmath22/packages/grii/metrics/"
:[font = input; startGroup; nowordwrap; ]
qload[newkerr]
:[font = print; inactive; formatted; output; endGroup; nowordwrap; ]
No Input Form Generated

;[o]
Default metric = newkerr
For the newkerr metric.
 
Coordinates
  1        2        3         4
 x  = r,  x  = u,  x  = ph,  x  = t
For the newkerr metric.
 
Line element

                       2    2       2   2    2
   2   -4 dph dt m r (a  - u )    dr  (r  + u )
ds   = ----------------------- + --------------- + 
                 2    2           2            2
             a (r  + u )         a  - 2 m r + r
 
    2   2    2
  du  (r  + u )     2        2 m r
  ------------- + dt  (-1 + -------) + 
      2    2                 2    2
     a  - u                 r  + u
 
                                    2    2
     2   2    2    2    2   2 m r (a  - u )
  dph  (a  - u ) (a  + r  + ---------------)
                                 2    2
                                r  + u
  ------------------------------------------
                       2
                      a
:[font = input; startGroup; nowordwrap; ]
grdefine["diRiem",{},"g{^a ^b}*R{c d ^e ^f ; a}*R{e f ^c ^d ; b}"]
:[font = message; inactive; formatted; output; endGroup; nowordwrap; ]
Can't Format Cell


;[o]
grii::create: Created a definition for diRiem
:[font = input; startGroup; nowordwrap; ]
grcalc[g[up,up]]
:[font = print; inactive; formatted; output; endGroup; nowordwrap; ]
No Input Form Generated

;[o]
For the newkerr metric.
Calculated g[up, up]( 1.54 sec.)
CPU Time = 1.65 sec.
:[font = input; startGroup; nowordwrap; ]
grmap[Factor,$]
:[font = print; inactive; formatted; output; endGroup; nowordwrap; ]
No Input Form Generated

;[o]
For the newkerr metric.
Applying Factor to g[up, up]
CPU Time = 0.17 sec.
:[font = input; startGroup; nowordwrap; ]
grcalc[{Chr[dn,dn,up],R[dn,dn,up,up]}]
:[font = print; inactive; formatted; output; endGroup; nowordwrap; ]
No Input Form Generated

;[o]
Created a definition for R[dn, dn, up, up]
For the newkerr metric.
Calculated g[dn, dn, pdn]( 0.22 sec.)
Calculated Chr[dn, dn, dn]( 0.28 sec.)
Calculated Chr[dn, dn, up]( 0.77 sec.)
Calculated R[dn, dn, dn, dn]( 3.85 sec.)
Calculated R[dn, dn, up, up]( 2.47 sec.)
CPU Time = 7.97 sec.
:[font = input; startGroup; nowordwrap; ]
grmap[Factor,$]
:[font = print; inactive; formatted; output; endGroup; nowordwrap; ]
No Input Form Generated

;[o]
For the newkerr metric.
Applying Factor to Chr[dn, dn, up]
Applying Factor to R[dn, dn, up, up]
CPU Time = 1.38 sec.
:[font = input; startGroup; nowordwrap; ]
grcalc[R[dn,dn,up,up,cdn]]
:[font = print; inactive; formatted; output; endGroup; nowordwrap; ]
No Input Form Generated

;[o]
For the newkerr metric.
Calculated R[dn, dn, up, up, cdn]( 80.3 sec.)
CPU Time = 80.52 sec.
:[font = input; startGroup; nowordwrap; ]
grmap[Factor,$]
:[font = print; inactive; formatted; output; endGroup; nowordwrap; ]
No Input Form Generated

;[o]
For the newkerr metric.
Applying Factor to R[dn, dn, up, up, cdn]
CPU Time = 12.19 sec.
:[font = input; startGroup; nowordwrap; ]
grcalc[diRiem]
:[font = print; inactive; formatted; output; endGroup; nowordwrap; ]
No Input Form Generated

;[o]
For the newkerr metric.
Calculated diRiem( 23.39 sec.)
CPU Time = 23.5 sec.
:[font = input; startGroup; nowordwrap; ]
grmap[Factor,$]
:[font = print; inactive; formatted; output; endGroup; nowordwrap; ]
No Input Form Generated

;[o]
For the newkerr metric.
Applying Factor to diRiem
CPU Time = 0.11 sec.
:[font = input; nowordwrap; ]
u:=a*Cos[th]
:[font = input; startGroup; nowordwrap; ]
grdisplay[$]
:[font = print; inactive; formatted; output; endGroup; nowordwrap; ]
No Input Form Generated

;[o]
For the newkerr metric.
 
diRiem

               2            2    2        2
diRiem = (720 m  (-2 m r + r  + a  Cos[th] ) 
 
      4        3              2  2        2
    (r  + 4 a r  Cos[th] - 6 a  r  Cos[th]  - 
 
         3          3    4        4
      4 a  r Cos[th]  + a  Cos[th] ) 
 
      4        3              2  2        2
    (r  - 4 a r  Cos[th] - 6 a  r  Cos[th]  + 
 
         3          3    4        4       2    2        2 9
      4 a  r Cos[th]  + a  Cos[th] )) / (r  + a  Cos[th] )
:[font = input; startGroup; nowordwrap; ]
MaxMemoryUsed[]
:[font = output; inactive; formatted; output; endGroup; nowordwrap; ]
1567992


;[o]
1567992
:[font = input; startGroup; nowordwrap; ]
TimeUsed[]
:[font = output; inactive; formatted; output; endGroup; nowordwrap; ]
133.14


;[o]
133.14
^*)