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{SECT 0 {PARA 18 "" 0 "" {TEXT -1 23 "Catalogue of Spacetimes" }}
{PARA 19 "" 0 "" {TEXT -1 27 "Thomas Mueller, Frank Grave" }}{PARA 0 "
" 0 "" {TEXT 256 66 "Schwarzschild metric in Schwarzschild coordinates
 (t,r,theta,phi)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 16 "Date: 20.04.2009" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "restart:grtw();" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#%=GRTensorII~Version~1.79~(R4)G" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#%06~February~2001G" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#%ZDeveloped~by~Peter~Musgrave,~Denis~Pollney~and~Kayll~LakeG" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%DCopyright~1994-2001~by~the~authors.G
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%inLatest~version~available~from:~
http://grtensor.phy.queensu.ca/G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%B
/home/muelleta/local/Grii/metricsG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "makeg(schwarzschild);" }}{PARA 6 "" 1 "" {TEXT -1 0 "
" }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 46 "Make
g 2.0: GRTensor metric/basis entry utility" }}{PARA 6 "" 1 "" {TEXT 
-1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 41 "To quit makeg, type 'exit' at \+
any prompt." }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT 
-1 44 "Do you wish to enter a 1) metric [g(dn,dn)]," }}{PARA 6 "" 1 "
" {TEXT -1 44 "                       2) line element [ds]," }}{PARA 
6 "" 1 "" {TEXT -1 63 "                       3) non-holonomic basis [
e(1)...e(n)], or" }}{PARA 6 "" 1 "" {TEXT -1 49 "                     \+
  4) NP tetrad [l,n,m,mbar]?" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 2 "2:" }}{PARA 6 "" 1 "" 
{TEXT -1 50 "Enter coordinates as a LIST (eg. [t,r,theta,phi]):" }}}
{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 16 "[t,r,theta,phi]:" }}
{PARA 6 "" 1 "" {TEXT -1 64 "Enter the line element using d[coord] to \+
indicate differentials." }}{PARA 6 "" 1 "" {TEXT -1 55 "(for example, \+
 r^2*(d[theta]^2 + sin(theta)^2*d[phi]^2)" }}{PARA 6 "" 1 "" {TEXT -1 
27 "[Type 'exit' to quit makeg]" }}{PARA 6 "" 1 "" {TEXT -1 8 " ds^2 =
 " }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 76 "-(1-rs/r)*c^2*d[t]
^2+d[r]^2/(1-rs/r)+r^2*(d[theta]^2+sin(theta)^2*d[phi]^2):" }}{PARA 6 
"" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 67 "If there are any \+
complex valued coordinates, constants or functions" }}{PARA 6 "" 1 "" 
{TEXT -1 66 "for this spacetime, please enter them as a SET ( eg. \{ z
, psi \} )." }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT 
-1 33 "Complex quantities [default=\{\}]: " }}}{EXCHG {PARA 0 "makeg>
" 0 "" {MPLTEXT 1 0 3 "\{\}:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%AThe~
values~you~have~entered~are:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%,Co
ordinatesG7&%\"tG%\"rG%&thetaG%$phiG" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#%(Metric:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%\"gG6#%\"aG\"\"\"
&%!G6#%\"bGF)K%'matrixG6#7&7&,&*$)%\"cG\"\"#F)!\"\"*(F6F7%#rsGF)%\"rGF
8F)\"\"!F<F<7&F<*&F)F),&F)F)*&F:F)F;F8F8F8F<F<7&F<F<*$)F;F7F)F<7&F<F<F
<*&FCF))-%$sinG6#%&thetaGF7F)Q(pprint06\"" }}{PARA 6 "" 1 "" {TEXT -1 
54 "You may choose to 0) Use the metric WITHOUT saving it," }}{PARA 6 
"" 1 "" {TEXT -1 46 "                  1) Save the metric as it is," }
}{PARA 6 "" 1 "" {TEXT -1 54 "                  2) Correct an element \+
of the metric," }}{PARA 6 "" 1 "" {TEXT -1 41 "                  3) Re
-enter the metric," }}{PARA 6 "" 1 "" {TEXT -1 54 "                  4
) Add/change constraint equations, " }}{PARA 6 "" 1 "" {TEXT -1 47 "  \+
                5) Add a text description, or" }}{PARA 6 "" 1 "" 
{TEXT -1 61 "                  6) Abandon this metric and return to Ma
ple." }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "makeg>" 0 "" 
{MPLTEXT 1 0 2 "0:" }}{PARA 6 "" 1 "" {TEXT -1 47 "Calculated ds for s
chwarzschild (0.000000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%2Def
ault~spacetimeG%.schwarzschildG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%AF
or~the~schwarzschild~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%,
CoordinatesG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"xG6#%#upG" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/)%#x~G%\"aGK%'vectorG6#7&%\"tG%\"rG%&
thetaG%$phiGQ(pprint16\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%-Line~ele
mentG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*$)%$~dsG\"\"#\"\"\",**(,&*$
)%\"cGF'F(!\"\"*(F.F'%#rsGF(%\"rGF/F(F(%#~dGF()%\"tG%#2~GF(F(*(,&F(F(*
&F1F(F2F/F/F/F3F()F2F6F(F(*()F2F'F(F3F()%&thetaGF6F(F(**F<F()-%$sinG6#
F>F'F(F3F()%$phiGF6F(F(" }}{PARA 6 "" 1 "" {TEXT -1 18 "makeg() comple
ted." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "grcalcd(Chr2);" }}
{PARA 6 "" 1 "" {TEXT -1 49 "Calculated detg for schwarzschild (0.0000
00 sec.)" }}{PARA 6 "" 1 "" {TEXT -1 53 "Calculated g(up,up) for schwa
rzschild (0.000000 sec.)" }}{PARA 6 "" 1 "" {TEXT -1 57 "Calculated g(
dn,dn,pdn) for schwarzschild (0.004000 sec.)" }}{PARA 6 "" 1 "" {TEXT 
-1 58 "Calculated Chr(dn,dn,dn) for schwarzschild (0.000000 sec.)" }}
{PARA 6 "" 1 "" {TEXT -1 58 "Calculated Chr(dn,dn,up) for schwarzschil
d (0.000000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"#
7!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%AFor~the~schwarzschild~space
time:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%aoChristoffel~symbol~of~the
~second~kind~(symmetric~in~first~two~indices)G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/*&&%&GammaG6#*&%\"tG\"\"\"%\"tGF*F*)%!G%\"rGF*,$*,\"\"
#!\"\",&%\"rGF*%#rsGF2F*F4!\"$%\"cGF1F5F*F*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/*&&%&GammaG6#*&%\"tG\"\"\"%\"rGF*F*)%!G%\"tGF*,$**\"\"
#!\"\"%\"rGF2,&F3F*%#rsGF2F2F5F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
/*&&%&GammaG6#*&%\"rG\"\"\"%\"rGF*F*)%!G%\"rGF*,$**\"\"#!\"\"%\"rGF2,&
F3F*%#rsGF2F2F5F*F2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*
&%\"rG\"\"\"%&thetaGF*F*)%!G%&thetaGF**&F*F*%\"rG!\"\"" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%\"rG\"\"\"%$phiGF*F*)%!G%$phiGF**
&F*F*%\"rG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%&t
hetaG\"\"\"%&thetaGF*F*)%!G%\"rGF*,&%\"rG!\"\"%#rsGF*" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%&thetaG\"\"\"%$phiGF*F*)%!G%$phiG
F**&-%$sinG6#%&thetaG!\"\"-%$cosGF2F*" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#/*&&%&GammaG6#*&%$phiG\"\"\"%$phiGF*F*)%!G%\"rGF*,$*&,&%\"rGF*%#rsG
!\"\"F*)-%$sinG6#%&thetaG\"\"#F*F4" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
/*&&%&GammaG6#*&%$phiG\"\"\"%$phiGF*F*)%!G%&thetaGF*,$*&-%$sinG6#%&the
taGF*-%$cosGF3F*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "gr
calcd(Riemann);" }}{PARA 6 "" 1 "" {TEXT -1 59 "Calculated R(dn,dn,dn,
dn) for schwarzschild (0.000000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#/%*CPU~Time~G$\"\"!F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%AFor~the~
schwarzschild~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%2Covaria
nt~RiemannG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%#R~G6#**%\"tG\"\"\"%
\"rGF)%\"tGF)%\"rGF),$*(%\"cG\"\"#%#rsGF)%\"rG!\"$!\"\"" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#/&%#R~G6#**%\"tG\"\"\"%&thetaGF)%\"tGF)%&thetaGF
),$*,\"\"#!\"\",&%\"rGF)%#rsGF0F)F2!\"#%\"cGF/F3F)F)" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#/&%#R~G6#**%\"tG\"\"\"%$phiGF)%\"tGF)%$phiGF),$*&#F)
\"\"#F)*,,&%\"rGF)%#rsG!\"\"F)F3!\"#%\"cGF0F4F)-%$sinG6#%&thetaGF0F)F)
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%#R~G6#**%\"rG\"\"\"%&thetaGF)%
\"rGF)%&thetaGF),$*(\"\"#!\"\",&%\"rGF)%#rsGF0F0F3F)F0" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#/&%#R~G6#**%\"rG\"\"\"%$phiGF)%\"rGF)%$phiGF),$*&#
F)\"\"#F)*(,&%\"rGF)%#rsG!\"\"F5F4F)-%$sinG6#%&thetaGF0F)F5" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/&%#R~G6#**%&thetaG\"\"\"%$phiGF)%&thetaGF)%
$phiGF)*(%\"rGF))-%$sinG6#%&thetaG\"\"#F)%#rsGF)" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 15 "grcalcd(Ricci);" }}{PARA 6 "" 1 "" {TEXT -1 
53 "Calculated R(dn,dn) for schwarzschild (0.004000 sec.)" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"\"%!\"$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%AFor~the~schwarzschild~spacetime:G" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#%0Covariant~RicciG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#-%\"RG6$%#dnGF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%#R~G6#%\"aG\"
\"\"&%!G6#%\"bGF)%8All~components~are~zeroG" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 21 "grcalcd(Ricciscalar);" }}{PARA 6 "" 1 "" {TEXT -1 
56 "Calculated Ricciscalar for schwarzschild (0.000000 sec.)" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"\"!F&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%AFor~the~schwarzschild~spacetime:G" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#%-Ricci~scalarG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%
#R~G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "grcalcd(RiemSq
);" }}{PARA 6 "" 1 "" {TEXT -1 38 "Created definition for R(dn,dn,up,u
p) " }}{PARA 6 "" 1 "" {TEXT -1 59 "Calculated R(dn,dn,up,up) for schw
arzschild (0.004000 sec.)" }}{PARA 6 "" 1 "" {TEXT -1 51 "Calculated R
iemSq for schwarzschild (0.000000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/%*CPU~Time~G$\"#?!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%AFor~
the~schwarzschild~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%<Ful
l~Contraction~of~RiemannG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%#K~G,$*
(\"#7\"\"\"%\"rG!\"'%#rsG\"\"#F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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