(*^

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Mm2 95 kruskal

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<<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/"
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qload[krn]
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No Input Form Generated

;[o]
Default metric = krn
For the krn metric.
 
Coordinates
  1        2        3         4
 x  = u,  x  = v,  x  = th,  x  = ph
For the krn metric.
 
Line element

                  2
   2   -16 du dv m  (2 m - r[u, v])      2        2
ds   = ---------------------------- + dth  r[u, v]  + 
               u v r[u, v]
 
     2        2        2
  dph  r[u, v]  Sin[th]
For the krn metric.
 
Text Information

Text  =     Null form of Kruskal metric    
For the krn metric.
 
Constraints 

                 (1,0)          -2 m (2 m - r[u, v])
constraints  = {r     [u, v] -> --------------------, 
                                     u r[u, v]
 
   (0,1)          -2 m (2 m - r[u, v])
  r     [u, v] -> --------------------, 
                       v r[u, v]
 
   (2,0)
  r     [u, v] -> 
 
            3      2                      2          3
   -2 m (8 m  - 4 m  r[u, v] - 2 m r[u, v]  + r[u, v] )
   ----------------------------------------------------, 
                        2        3
                       u  r[u, v]
 
   (0,2)
  r     [u, v] -> 
 
            3      2                      2          3
   -2 m (8 m  - 4 m  r[u, v] - 2 m r[u, v]  + r[u, v] )
   ----------------------------------------------------, 
                        2        3
                       v  r[u, v]
 
                      3
   (1,1)          -8 m  (2 m - r[u, v])
  r     [u, v] -> ---------------------}
                                 3
                      u v r[u, v]
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grcalc[R[dn,dn]]
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No Input Form Generated

;[o]
For the krn metric.
Calculated g[up, up]( 0.27 sec.)
Calculated g[dn, dn, pdn]( 0.22 sec.)
Calculated Chr[dn, dn, dn]( 0.17 sec.)
Calculated Chr[dn, dn, up]( 0.33 sec.)
Calculated R[dn, dn]( 0.98 sec.)
CPU Time = 2.08 sec.
:[font = input; startGroup; nowordwrap; ]
grmap[ApplyConstraints,$]
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No Input Form Generated

;[o]
For the krn metric.
Applying ApplyConstraints to R[dn, dn]
CPU Time = 0.11 sec.
:[font = input; startGroup; nowordwrap; ]
grmap[Together[#,Trig->True]&,$]
:[font = print; inactive; formatted; output; endGroup; nowordwrap; ]
No Input Form Generated

;[o]
For the krn metric.
Applying Together[#1, Trig -> True] &  to R[dn, dn]
CPU Time = 0.33 sec.
:[font = input; startGroup; nowordwrap; ]
grdisplay[$]
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No Input Form Generated

;[o]
For the krn metric.
 
Covariant Ricci
R[dn, dn] = All components are zero
:[font = input; startGroup; nowordwrap; ]
grcalc[RiemSq]
:[font = print; inactive; formatted; output; endGroup; nowordwrap; ]
No Input Form Generated

;[o]
For the krn metric.
Calculated R[dn, dn, dn, dn]( 0.99 sec.)
Calculated R[up, up, dn, dn]( 1.1 sec.)
Calculated RiemSq( 3.84 sec.)
CPU Time = 6.04 sec.
:[font = input; startGroup; nowordwrap; ]
grmap[ApplyConstraints,$]
:[font = print; inactive; formatted; output; endGroup; nowordwrap; ]
No Input Form Generated

;[o]
For the krn metric.
Applying ApplyConstraints to RiemSq
CPU Time = 0.16 sec.
:[font = input; startGroup; nowordwrap; ]
grmap[Together[#,Trig->True]&,$]
:[font = print; inactive; formatted; output; endGroup; nowordwrap; ]
No Input Form Generated

;[o]
For the krn metric.
Applying Together[#1, Trig -> True] &  to RiemSq
CPU Time = 0.28 sec.
:[font = input; startGroup; nowordwrap; ]
grdisplay[$]
:[font = print; inactive; formatted; output; endGroup; nowordwrap; ]
No Input Form Generated

;[o]
For the krn metric.
 
Full Contraction of Riemann

          2
      48 m
K  = --------
            6
     r[u, v]
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MaxMemoryUsed[]
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1306284


;[o]
1306284
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TimeUsed[]
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14.00


;[o]
14.
^*)