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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 326 "Program for the hamilto
nian treatment of general relativity (ADM) based on the 3+1 split of s
pace-time. The program is adapted for numerical relativity purposes, s
o it's using extrinsic curvature instead of momentum components. Here \+
we have a version for DeSitter space-time and a scalar field coupled m
inimally with gravity. " }}{PARA 258 "" 0 "" {TEXT -1 6 "Author" }
{TEXT 256 60 " : D.N. Vulcanov - The West University of Timisoara, Rom
ania" }}{PARA 0 "" 0 "" {TEXT 257 4 "See " }{TEXT -1 2 ": " }{TEXT 
258 31 "gr-qc/0010085 , physics/0010053" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "
grtw();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%=GRTensorII~Version~1.77~(
R5)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%+3~May~2000G" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#%ZDeveloped~by~Peter~Musgrave,~Denis~Pollney~and~K
ayll~LakeG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%DCopyright~1994-2000~by
~the~authors.G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%inLatest~version~av
ailable~from:~http://grtensor.phy.queensu.ca/G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$%P/afs/aei-potsdam.mpg.de/u/vulcan/grii/mymetricsG%N/af
s/aei-potsdam.mpg.de/u/vulcan/grii/metricsG" }}}{EXCHG {PARA 260 "" 0 
"" {TEXT -1 57 "Some general definitions, before downloading the metri
c !" }}{PARA 0 "" 0 "" {TEXT 259 25 "The main notations are : " }}
{PARA 0 "" 0 "" {TEXT -1 43 "ha0              the hamiltonian constrai
nt" }}{PARA 0 "" 0 "" {TEXT -1 40 "ha(i)            the momentum const
raint" }}{PARA 0 "" 0 "" {TEXT -1 32 "Ni(i)           the shift vector
" }}{PARA 0 "" 0 "" {TEXT -1 35 "N                the lapse function" 
}}{PARA 0 "" 0 "" {TEXT -1 45 "g(i,j)           the three-dimensional \+
metric" }}{PARA 0 "" 0 "" {TEXT -1 39 "K(i,j)          the extrinsic c
urvature" }}{PARA 0 "" 0 "" {TEXT -1 55 "T(i,j)          components of
 the stress-energy tensor " }}{PARA 0 "" 0 "" {TEXT -1 66 "derge(i,j) \+
 the dynamic equation for the three-dimensional metric " }}{PARA 0 "" 
0 "" {TEXT -1 61 "derpi(i,j)   the dynamic equation for the momentum c
onponents" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 190 "grdef(`ha0:=R
icciscalar\{\}+K\{^i i\}*K\{^j j\}-K\{ i j \}*K\{^i ^j\}-2*(-(1/(N(t,r
,theta,phi)^2))*T00\{ \}-2*Ni\{ ^i \}*T0\{ i \}/(N(t,r,theta,phi)^2) +
 Ni\{ ^i \}*Ni\{ ^j \} *T\{ i j \}/(N(t,r,theta,phi)^2))`);" }}{PARA 
6 "" 1 "" {TEXT -1 53 "`Warning ` = (`No definition found for object` \+
= T00)" }}{PARA 6 "" 1 "" {TEXT -1 58 "`Warning ` = (`No definition fo
und for object` = K(up,dn))" }}{PARA 6 "" 1 "" {TEXT -1 58 "`Warning `
 = (`No definition found for object` = K(dn,dn))" }}{PARA 6 "" 1 "" 
{TEXT -1 58 "`Warning ` = (`No definition found for object` = K(up,up)
)" }}{PARA 6 "" 1 "" {TEXT -1 56 "`Warning ` = (`No definition found f
or object` = Ni(up))" }}{PARA 6 "" 1 "" {TEXT -1 56 "`Warning ` = (`No
 definition found for object` = T0(dn))" }}{PARA 6 "" 1 "" {TEXT -1 
58 "`Warning ` = (`No definition found for object` = T(dn,dn))" }}
{PARA 6 "" 1 "" {TEXT -1 26 "Created definition for ha0" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "grdef(`ha\{ i \}:=- K\{ ^j j ;i\} \+
+ K\{ ^j i ;j\}+T0\{ i \}/N(t,r,theta,phi) - Ni\{ ^j \}*T\{ i j \}/N(t
,r,theta,phi)`);" }}{PARA 6 "" 1 "" {TEXT -1 62 "`Warning ` = (`No def
inition found for object` = K(up,dn,cdn))" }}{PARA 6 "" 1 "" {TEXT -1 
56 "`Warning ` = (`No definition found for object` = Ni(up))" }}{PARA 
6 "" 1 "" {TEXT -1 56 "`Warning ` = (`No definition found for object` \+
= T0(dn))" }}{PARA 6 "" 1 "" {TEXT -1 58 "`Warning ` = (`No definition
 found for object` = T(dn,dn))" }}{PARA 6 "" 1 "" {TEXT -1 29 "Created
 definition for ha(dn)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "g
rdef(`derge\{ i j \}:=-2*N(t,r,theta,phi)*K\{ i j \} + Ni\{ j ;i\} + N
i\{ j ;i \}`);" }}{PARA 6 "" 1 "" {TEXT -1 60 "`Warning ` = (`No defin
ition found for object` = Ni(dn,cdn))" }}{PARA 6 "" 1 "" {TEXT -1 58 "
`Warning ` = (`No definition found for object` = K(dn,dn))" }}{PARA 6 
"" 1 "" {TEXT -1 35 "Created definition for derge(dn,dn)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "grdef(`Ndd\{ m j \}:= Nd\{ m ;j \}`
); " }}{PARA 6 "" 1 "" {TEXT -1 60 "`Warning ` = (`No definition found
 for object` = Nd(dn,cdn))" }}{PARA 6 "" 1 "" {TEXT -1 33 "Created def
inition for Ndd(dn,dn)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 373 "
grdef(`derpK\{ i j \}:=-2*N(t,r,theta,phi)*K\{ i l \}*K\{ ^l j \} + N(
t,r,theta,phi)*K\{ l ^l \}*K\{ i j \} +N(t,r,theta,phi)*R\{ i j \} - N
dd\{ i j \} + Ni\{ ^ l \}*K\{ i j ;l \} + K\{ l j \}*Ni\{ ^l ;i \} + K
\{ i l \}*Ni\{ ^l ;j \}-N(t,r,theta,phi)*T\{ i j \} + (1/2)*N(t,r,thet
a,phi)*g\{ i j \}*T\{ ^k k \} + (1/(2*N(t,r,theta,phi)))*g \{ i j \}*(
T00 + 2*Ni\{ ^p \}*T0\{ p \} - Ni\{ ^k \}*Ni\{ ^n \}*T\{ k n \})`);" }
}{PARA 6 "" 1 "" {TEXT -1 58 "`Warning ` = (`No definition found for o
bject` = K(up,dn))" }}{PARA 6 "" 1 "" {TEXT -1 58 "`Warning ` = (`No d
efinition found for object` = K(dn,dn))" }}{PARA 6 "" 1 "" {TEXT -1 
56 "`Warning ` = (`No definition found for object` = Ni(up))" }}{PARA 
6 "" 1 "" {TEXT -1 56 "`Warning ` = (`No definition found for object` \+
= T0(dn))" }}{PARA 6 "" 1 "" {TEXT -1 58 "`Warning ` = (`No definition
 found for object` = T(dn,dn))" }}{PARA 6 "" 1 "" {TEXT -1 62 "`Warnin
g ` = (`No definition found for object` = K(dn,dn,cdn))" }}{PARA 6 "" 
1 "" {TEXT -1 60 "`Warning ` = (`No definition found for object` = Ni(
up,cdn))" }}{PARA 6 "" 1 "" {TEXT -1 58 "`Warning ` = (`No definition \+
found for object` = K(dn,up))" }}{PARA 6 "" 1 "" {TEXT -1 58 "`Warning
 ` = (`No definition found for object` = T(up,dn))" }}{PARA 6 "" 1 "" 
{TEXT -1 35 "Created definition for derpK(dn,dn)" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 241 "grdef(`A:=-(1/N(t,r,theta,phi))^2*(diff(psi(
t,r,theta,phi),t))^2+(2/(N(t,r,theta,phi)^2))*Ni\{^i\}*diff(psi(t,r,th
eta,phi),t)*psid\{ i \} +(g\{ ^i ^j \} - Ni\{ ^i \}* Ni\{ ^j \}/(N(t,r
,theta,phi)^2) )*psid\{ i \}*psid\{ j \} + m^2 *psi(t,r,theta,phi)^2`)
;" }}{PARA 6 "" 1 "" {TEXT -1 56 "`Warning ` = (`No definition found f
or object` = Ni(up))" }}{PARA 6 "" 1 "" {TEXT -1 58 "`Warning ` = (`No
 definition found for object` = psid(dn))" }}{PARA 6 "" 1 "" {TEXT -1 
24 "Created definition for A" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 93 "grdef(`T00:=diff(psi(t,r,theta,phi),t)^2 +(1/2)*(N(t,r,theta,phi
)^2-Ni\{ ^j \}*Ni\{ j \})*A\{ \}`);" }}{PARA 6 "" 1 "" {TEXT -1 56 "`W
arning ` = (`No definition found for object` = Ni(dn))" }}{PARA 6 "" 
1 "" {TEXT -1 56 "`Warning ` = (`No definition found for object` = Ni(
up))" }}{PARA 6 "" 1 "" {TEXT -1 26 "Created definition for T00" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "grdef(`T\{ i j \}:=psid\{ i \+
\}*psid\{ j \} -(1/2)*g\{ i  j \}*A\{ \}`);" }}{PARA 6 "" 1 "" {TEXT 
-1 58 "`Warning ` = (`No definition found for object` = psid(dn))" }}
{PARA 6 "" 1 "" {TEXT -1 31 "Created definition for T(dn,dn)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "grdef(`T0\{ i \} := diff(psi
(t,r,theta,phi),t)*psid\{ i \} - Ni\{ i \} *A\{ \}`);" }}{PARA 6 "" 1 
"" {TEXT -1 56 "`Warning ` = (`No definition found for object` = Ni(dn
))" }}{PARA 6 "" 1 "" {TEXT -1 58 "`Warning ` = (`No definition found \+
for object` = psid(dn))" }}{PARA 6 "" 1 "" {TEXT -1 29 "Created defini
tion for T0(dn)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "qload(de
sitter_sf);" }}{PARA 6 "" 1 "" {TEXT -1 46 "Calculated ds for desitter
_sf (0.000000 sec.) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%2Default~spa
cetimeG%,desitter_sfG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?For~the~des
itter_sf~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%\"aG-%'vectorG6#7%%\"rG%&thetaG%$phiG" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%-Line~elementG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/*$)%$~dsG\"\"#\"\"\",(**%\"aG\"\"\")%\"tG#\"\"%\"\"$F(
%#~dGF,)%\"rG%#2~GF,F,*()F4F'F(F2F()%&thetaGF5F,F,**F7F()-%$sinG6#F9F'
F(F2F()%$phiGF5F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "grca
lc(metric);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"\"\"!\"
$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "grdisplay(metric);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%?For~the~desitter_sf~spacetime:G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%8Covariant~metric~tensorG" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#-%\"gG6$%#dnGF&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/*&&%#g~G6#%\"aG\"\"\"&%!G6#%\"bGF)-%'matrixG6#7%7%*&F(
F))%\"tG#\"\"%\"\"$\"\"\"\"\"!F:7%F:*$)%\"rG\"\"#F9F:7%F:F:*&F=F9)-%$s
inG6#%&thetaGF?F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "grdef
(`psid\{ i \} := [diff(psi(t,r,theta,phi),r),diff(psi(t,r,theta,phi),t
heta),diff(psi(t,r,theta,phi),phi)]`);" }}{PARA 6 "" 1 "" {TEXT -1 43 
"Components assigned for metric: desitter_sf" }}{PARA 6 "" 1 "" {TEXT 
-1 31 "Created definition for psid(dn)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "grcalc(psid(dn));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
/%*CPU~Time~G$\"\"\"!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 
"grdisplay(psid(dn));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?For~the~des
itter_sf~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%)psid(dn)G" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%%psidG6#%#dnG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/&%%psidG6#%\"aG-%'vectorG6#7%-%%diffG6$-%$psiG6&%\"tG%
\"rG%&thetaG%$phiGF3-F-6$F/F4-F-6$F/F5" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 105 "grdef(`Nd\{ ^ m \} := [diff(N(t,r,theta,phi),r),diff
(N(t,r,theta,phi),theta),diff(N(t,r,theta,phi),phi)]`);" }}{PARA 6 "" 
1 "" {TEXT -1 43 "Components assigned for metric: desitter_sf" }}
{PARA 6 "" 1 "" {TEXT -1 29 "Created definition for Nd(up)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "grcalc(Nd(up));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#/%*CPU~Time~G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "grdisplay(Nd(up));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#%?For~the~desitter_sf~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
%'Nd(up)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%#NdG6#%#upG" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/)%#NdG%\"aG-%'vectorG6#7%-%%diffG6$-%\"NG6&
%\"tG%\"rG%&thetaG%$phiGF2-F,6$F.F3-F,6$F.F4" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 40 "Ni=0 ! Skip this line if do not use it !" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "grdef(`Ni\{ ^i \} := [0, 0, 0]`);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "grdef(`Ni\{ ^i \} := [N1(
t,r,theta,phi), N2(t,r,theta,phi), N3(t,r,theta,phi)]`);" }}{PARA 6 "
" 1 "" {TEXT -1 43 "Components assigned for metric: desitter_sf" }}
{PARA 6 "" 1 "" {TEXT -1 29 "Created definition for Ni(up)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "grdef(`vi1\{ i \}:=[Ka(t,r,theta,ph
i),0,0]`);" }}{PARA 6 "" 1 "" {TEXT -1 43 "Components assigned for met
ric: desitter_sf" }}{PARA 6 "" 1 "" {TEXT -1 30 "Created definition fo
r vi1(dn)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "grdef(`vi3\{ i
 \}:=[0,0,Kc(t,r,theta,phi)]`);" }}{PARA 6 "" 1 "" {TEXT -1 43 "Compon
ents assigned for metric: desitter_sf" }}{PARA 6 "" 1 "" {TEXT -1 30 "
Created definition for vi3(dn)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 43 "grdef(`vi2\{ i \}:=[0,Kb(t,r,theta,phi),0]`);" }}{PARA 6 "" 1 
"" {TEXT -1 43 "Components assigned for metric: desitter_sf" }}{PARA 
6 "" 1 "" {TEXT -1 30 "Created definition for vi2(dn)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "grdef(`K\{ i j \} := (vi1\{ i \}*kd
elta\{j $r\}+vi2\{ i \}*kdelta\{ j$theta \}+vi3\{ i \}*kdelta\{j $phi
\})`);" }}{PARA 6 "" 1 "" {TEXT -1 31 "Created definition for K(dn,dn)
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "grcalc(K(dn,dn));" }}
{PARA 6 "" 1 "" {TEXT -1 56 "Calculated kdelta(dn,dn) for desitter_sf \+
(.001000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 51 "Calculated K(dn,dn) fo
r desitter_sf (.002000 sec.) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CP
U~Time~G$\"\"&!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "grdis
play(K(dn,dn));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?For~the~desitter_
sf~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%)K(dn,dn)G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"KG6$%#dnGF&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/*&&%\"KG6#%\"aG\"\"\"&%!G6#%\"bGF)-%'matrixG6#7%7%-%#K
aG6&%\"tG%\"rG%&thetaG%$phiG\"\"!F:7%F:-%#KbGF5F:7%F:F:-%#KcGF5" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Now the calculations !" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "grcalc(ha0);" }}{PARA 6 "" 1 "" 
{TEXT -1 30 "Created definition for Ni(dn) " }}{PARA 6 "" 1 "" {TEXT 
-1 32 "Created definition for K(up,dn) " }}{PARA 6 "" 1 "" {TEXT -1 
32 "Created definition for K(up,up) " }}{PARA 6 "" 1 "" {TEXT -1 47 "C
alculated detg for desitter_sf (.001000 sec.) " }}{PARA 6 "" 1 "" 
{TEXT -1 51 "Calculated g(up,up) for desitter_sf (.001000 sec.) " }}
{PARA 6 "" 1 "" {TEXT -1 44 "Calculated A for desitter_sf (.002000 sec
.) " }}{PARA 6 "" 1 "" {TEXT -1 50 "Calculated Ni(dn) for desitter_sf \+
(0.000000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 46 "Calculated T00 for de
sitter_sf (.008000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 55 "Calculated g
(dn,dn,pdn) for desitter_sf (.003000 sec.) " }}{PARA 6 "" 1 "" {TEXT 
-1 56 "Calculated Chr(dn,dn,dn) for desitter_sf (.002000 sec.) " }}
{PARA 6 "" 1 "" {TEXT -1 56 "Calculated Chr(dn,dn,up) for desitter_sf \+
(.003000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 51 "Calculated R(dn,dn) fo
r desitter_sf (.003000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 55 "Calculat
ed Ricciscalar for desitter_sf (0.000000 sec.) " }}{PARA 6 "" 1 "" 
{TEXT -1 51 "Calculated K(up,dn) for desitter_sf (.002000 sec.) " }}
{PARA 6 "" 1 "" {TEXT -1 51 "Calculated K(up,up) for desitter_sf (.001
000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 49 "Calculated T0(dn) for desit
ter_sf (.007000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 51 "Calculated T(dn
,dn) for desitter_sf (.007000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 46 "C
alculated ha0 for desitter_sf (.014000 sec.) " }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/%*CPU~Time~G$\"$,\"!\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "gralter(ha0,sqrt,simplify);" }}{PARA 6 "" 1 "" {TEXT 
-1 48 "Component simplification of a GRTensorII object:" }}{PARA 6 "" 
1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 47 "Applying routine `s
implify[sqrt]` to object ha0" }}{PARA 6 "" 1 "" {TEXT -1 39 "Applying \+
routine simplify to object ha0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*C
PU~Time~G$\"%?6!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "gral
ter(ha0,trigsin,expand);" }}{PARA 6 "" 1 "" {TEXT -1 48 "Component sim
plification of a GRTensorII object:" }}{PARA 6 "" 1 "" {TEXT -1 1 " " 
}}{PARA 6 "" 1 "" {TEXT -1 50 "Applying routine `simplify[trigsin]` to
 object ha0" }}{PARA 6 "" 1 "" {TEXT -1 37 "Applying routine expand to
 object ha0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"$H\"!\"
$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "grdisplay(ha0);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%?For~the~desitter_sf~spacetime:G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%$ha0G" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/%$ha0G%J~6603~words.~Exceeds~grOptionDisplayLimitG" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "grcalc(ha(dn));" }}{PARA 6 "" 1 "" 
{TEXT -1 40 "Created a definition for    K(up,dn,cdn)" }}{PARA 6 "" 1 
"" {TEXT -1 55 "Calculated K(up,dn,cdn) for desitter_sf (.009000 sec.)
 " }}{PARA 6 "" 1 "" {TEXT -1 49 "Calculated ha(dn) for desitter_sf (.
015000 sec.) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"$>\"!
\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "gralter(ha(dn),sqrt,
simplify);" }}{PARA 6 "" 1 "" {TEXT -1 48 "Component simplification of
 a GRTensorII object:" }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 
1 "" {TEXT -1 50 "Applying routine `simplify[sqrt]` to object ha(dn)" 
}}{PARA 6 "" 1 "" {TEXT -1 42 "Applying routine simplify to object ha(
dn)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"%W5!\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "gralter(ha(dn),trigsin,expan
d);" }}{PARA 6 "" 1 "" {TEXT -1 48 "Component simplification of a GRTe
nsorII object:" }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" 
{TEXT -1 53 "Applying routine `simplify[trigsin]` to object ha(dn)" }}
{PARA 6 "" 1 "" {TEXT -1 40 "Applying routine expand to object ha(dn)
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"$=\"!\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "grdisplay(ha(dn));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%?For~the~desitter_sf~spacetime:G" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%'ha(dn)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#-%#haG6#%#dnG" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/&%#haG6#%\"rG,N*&*,
%\"aG\"\"\")%\"tG#\"\"%\"\"$\"\"\")-%#N1G6&F.F'%&thetaG%$phiG\"\"#F2-%
%diffG6$-%$psiGF6F.F,-F;6$F=F'F,F2*$)-%\"NGF6\"\"$F2!\"\"!\"\"*&*(-%#N
3GF6F,-F;6$F=F8F,F?F2F2FCFFFG*&*,F+F2F-F2F4F,)%\"mGF9F2)F=F9F2F2FCFF#F
GF9*&**F+F2F-F2F4F2)F:F9F2F2*$)FC\"\"$F2FF#F,F9*&-%#KaGF6F2*(F'\"\"\"F
+\"\"\")F.#\"\"%F1F2FFF9*&*.F+F2F-F2F4F2FJF2F:F2FLF2F2*$)FC\"\"$F2FFFG
*&*0F+F2F-F2F4F2-F;6$F=F7F,FLF2-%#N2GF6F,FJF2F2*$)FC\"\"$F2FFF,*&*&F4F
2)F?F9F2F2FCFF#!\"$F9*&**F+F2F-F2F4F2)FeoF9F2F2*&FC\"\"\")F'\"\"#F2FFF
S*&**F+F2F-F2F^pF2)F4F1F2F2*$)FC\"\"$F2FFFZ*&*.F+F2F-F2F?F2FeoF2F3F2Fg
oF2F2*$)FC\"\"$F2FFF,*&*,F+F2F-F2F4F2FcpF2)FgoF9F2F2*$)FC\"\"$F2FFFZ*&
*.F+F2F-F2F?F2FLF2F3F2FJF2F2*$)FC\"\"$F2FFF,*&*.F+F2F-F2F4F2FgoF2F:F2F
eoF2F2*$)FC\"\"$F2FFFG*&*,F+F2F-F2F4F2)FLF9F2)FJF9F2F2*$)FC\"\"$F2FFFZ
*&**F+F2F-F2F4F2FerF2F2*(FC\"\"\")F'\"\"#F2)-%$sinG6#F7\"\"#F2FFFS*&-%
#KcGF6F2*&)F'\"\"$F2)Fas\"\"#F2FFF,*&-%#KbGF6F2*$)F'\"\"$F2FFF,*&-F;6$
F^tF'F2*$)F'\"\"#F2FFFG*&-F;6$FfsF'F2*&)F'\"\"#F2)Fas\"\"#F2FFFG*&*(Fg
oF2FeoF2F?F2F2FCFFFG*&*&F:F2F?F2F2FCFFF," }}{PARA 12 "" 1 "" {XPPMATH 
20 "6#/&%#haG6#%&thetaG,L*&*()%\"rG\"\"#\"\"\"-%#N2G6&%\"tGF,F'%$phiG
\"\"\")-%%diffG6$-%$psiGF1F,F-F.F.*(-%\"NGF1\"\"\"%\"aG\"\"\")F2#\"\"%
\"\"$F.!\"\"#!\"\"F-*&-F76$-%#KaGF1F'F.*&F?\"\"\")F2#\"\"%FDF.FEFG*&*,
F+F.F/F.-%#N1GF1F4-F76$F9F2F4F6F4F.*$)F<\"\"$F.FEFG*&*(-%#N3GF1F4-F76$
F9F3F4-F76$F9F'F4F.F<FEFG*&*(F+F.F/F.)FVF-F.F.*$)F<\"\"$F.FE#F4F-*&*&F
VF.F[oF.F.F<FEF4*&*&-%#KbGF1F4-%$cosGF&F4F.*&)F,\"\"#F.-%$sinGF&\"\"\"
FEF4*&*(FTF.F[oF.F6F.F.F<FEFG*&*,F+F.F/F.FgnF.FVF.FinF.F.*$)F<\"\"$F.F
EFG*&*,F+F.F[oF.FinF.)F/F-F.FgnF.F.*$)F<\"\"$F.FEF4*&**F+F.F[qF.FVF.F[
oF.F.*$)F<\"\"$F.FEFG*&*.F+F.F/F.F6F.FinF.FTF.FgnF.F.*$)F<\"\"$F.FEF4*
&*&-%#KcGF1F4FjoF.F.*&)F,\"\"#F.)F_p\"\"$F.FEF4*&-F76$F[rF'F.*&)F,\"\"
#F.)F_p\"\"#F.FEFG*&*&F/F.)FinF-F.F.*&F<\"\"\")F_p\"\"#F.FEFF*&*&F/F.)
F[oF-F.F.F<FE#!\"$F-*&*,F+F.F6F.F[oF.FTF.F[qF.F.*$)F<\"\"$F.FEF4*&**F+
F.F/F.)%\"mGF-F.)F9F-F.F.F<FEFF*&*(F+F.FcsF.)F/FDF.F.*$)F<\"\"$F.FEFco
*&**F+F.F/F.F\\sF.)FgnF-F.F.*$)F<\"\"$F.FEFco*&**F+F.F/F.F5F.)FTF-F.F.
*$)F<\"\"$F.FEFco" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/&%#haG6#%$phiG,H
*&-%%diffG6$-%#KaG6&%\"tG%\"rG%&thetaGF'F'\"\"\"*&%\"aG\"\"\")F0#\"\"%
\"\"$F3!\"\"!\"\"*&*&-F+6$-%$psiGF/F0\"\"\"-F+6$FAF'FCF3-%\"NGF/F;FC*&
*(-%#N1GF/FCFDF3-F+6$FAF1FCF3FFF;F<*&-F+6$-%#KbGF/F'F3*$)F1\"\"#F3F;F<
*&*(-%#N2GF/FCFDF3-F+6$FAF2FCF3FFF;F<*&*&-%#N3GF/FC)FD\"\"#F3F3FFF;#!
\"$F[o*&*.)F1F[oF3FLF3FDF3FJF3)FhnF[oF3)-%$sinG6#F2F[oF3F3*$)FF\"\"$F3
F;FC*&*0F`oF3FhnF3FLF3FZF3FJF3FXF3FboF3F3*$)FF\"\"$F3F;FC*&*(FhnF3)FZF
[oF3FboF3F3FFF;#F<F[o*&*.F`oF3FhnF3FXF3F?F3FZF3FboF3F3*$)FF\"\"$F3F;F<
*&*,F`oF3FhnF3F`pF3)FXF[oF3FboF3F3*$)FF\"\"$F3F;#FCF[o*&*.F`oF3FZF3FDF
3FXF3FaoF3FboF3F3*$)FF\"\"$F3F;FC*&**F`oF3FjnF3)FhnF:F3FboF3F3*$)FF\"
\"$F3F;F]q*&**F`oF3FhnF3)F?F[oF3FboF3F3*$)FF\"\"$F3F;F]q*&*,F`oF3FaoF3
F?F3FDF3FboF3F3*$)FF\"\"$F3F;F<*&*,F`oF3FhnF3)%\"mGF[oF3)FAF[oF3FboF3F
3FFF;Fap*&*.F`oF3FhnF3FJF3F?F3FLF3FboF3F3*$)FF\"\"$F3F;F<*&*,F`oF3FhnF
3)FLF[oF3)FJF[oF3FboF3F3*$)FF\"\"$F3F;F]q*&**F`oF3FhnF3F`sF3FboF3F3*(F
F\"\"\"F5\"\"\")F0#\"\"%F:F3F;Fap" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "grcalc(derge(dn,dn));" }}{PARA 6 "" 1 "" {TEXT -1 38 
"Created a definition for    Ni(dn,cdn)" }}{PARA 6 "" 1 "" {TEXT -1 
53 "Calculated Ni(dn,cdn) for desitter_sf (.005000 sec.) " }}{PARA 6 "
" 1 "" {TEXT -1 55 "Calculated derge(dn,dn) for desitter_sf (.002000 s
ec.) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"#s!\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "gralter(derge(dn,dn),sqrt,tr
ingsin,simplify);" }}{PARA 6 "" 1 "" {TEXT -1 48 "Component simplifica
tion of a GRTensorII object:" }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}
{PARA 6 "" 1 "" {TEXT -1 48 "Applying routine simplify to object derge
(dn,dn)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"#e!\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "grdisplay(derge(dn,dn));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%?For~the~desitter_sf~spacetime:G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%-derge(dn,dn)G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%&dergeG6$%#dnGF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/
*&&%&dergeG6#%\"rG\"\"\"&%!GF'F),&*&-%\"NG6&%\"tGF(%&thetaG%$phiGF)-%#
KaGF0F)!\"#*(%\"aGF))F1#\"\"%\"\"$\"\"\"-%%diffG6$-%#N1GF0F(F)\"\"#" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&dergeG6#%&thetaG\"\"\"&%!G6#%\"
rGF),&*(%\"aGF))%\"tG#\"\"%\"\"$\"\"\"-%%diffG6$-%#N1G6&F2F-F(%$phiGF(
F)\"\"#*&F-F)-%#N2GF<F)!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&d
ergeG6#%$phiG\"\"\"&%!G6#%\"rGF),(*(%\"aGF))%\"tG#\"\"%\"\"$\"\"\"-%%d
iffG6$-%#N1G6&F2F-%&thetaGF(F(F)\"\"#*&F-F)-%#N3GF<F)!\"#*(F-F6F@F6)-%
$cosG6#F=F>F6F>" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&dergeG6#%\"rG
\"\"\"&%!G6#%&thetaGF),&*&F(F)-%#N2G6&%\"tGF(F-%$phiGF)\"\"#*&)F(F5\"
\"\"-%%diffG6$F0F(F)F5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&dergeG
6#%&thetaG\"\"\"&%!GF'F),(*&-%\"NG6&%\"tG%\"rGF(%$phiGF)-%#KbGF0F)!\"#
*&)F2\"\"#\"\"\"-%%diffG6$-%#N2GF0F(F)F9*&-%#N1GF0F)F2F)F9" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/*&&%&dergeG6#%$phiG\"\"\"&%!G6#%&thetaGF),&
*&)%\"rG\"\"#\"\"\"-%%diffG6$-%#N2G6&%\"tGF1F-F(F(F)F2**F0F3-%$sinGF,F
)-%#N3GF9F)-%$cosGF,F)!\"#" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/*&&%&de
rgeG6#%\"rG\"\"\"&%!G6#%$phiGF),**&F(F)-%#N3G6&%\"tGF(%&thetaGF-F)\"\"
#*(F(\"\"\"F0F7)-%$cosG6#F4F5F7!\"#*&)F(F5F7-%%diffG6$F0F(F)F5*(F>F7F?
F7F8F7F<" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&dergeG6#%&thetaG\"\"
\"&%!G6#%$phiGF),(**)%\"rG\"\"#\"\"\"-%$sinGF'F)-%#N3G6&%\"tGF1F(F-F)-
%$cosGF'F)F2*&F0F3-%%diffG6$F6F(F)F2*(F0F3F=F3)F:F2F3!\"#" }}{PARA 12 
"" 1 "" {XPPMATH 20 "6#/*&&%&dergeG6#%$phiG\"\"\"&%!GF'F),.*&-%\"NG6&%
\"tG%\"rG%&thetaGF(F)-%#KcGF0F)!\"#*&)F2\"\"#\"\"\"-%%diffG6$-%#N3GF0F
(F)F9*(F8F:F;F:)-%$cosG6#F3F9F:F6*&-%#N1GF0F)F2F)F9*(FFF:F2F:FAF:F6**F
8F:-%#N2GF0F)-%$sinGFDF)FBF)F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 21 "grcalc(derpK(dn,dn));" }}{PARA 6 "" 1 "" {TEXT -1 30 "Created \+
definition for Nd(dn) " }}{PARA 6 "" 1 "" {TEXT -1 38 "Created a defin
ition for    Nd(dn,cdn)" }}{PARA 6 "" 1 "" {TEXT -1 40 "Created a defi
nition for    K(dn,dn,cdn)" }}{PARA 6 "" 1 "" {TEXT -1 38 "Created a d
efinition for    Ni(up,cdn)" }}{PARA 6 "" 1 "" {TEXT -1 32 "Created de
finition for K(dn,up) " }}{PARA 6 "" 1 "" {TEXT -1 32 "Created definit
ion for T(up,dn) " }}{PARA 6 "" 1 "" {TEXT -1 49 "Calculated Nd(dn) fo
r desitter_sf (.001000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 53 "Calculat
ed Nd(dn,cdn) for desitter_sf (.004000 sec.) " }}{PARA 6 "" 1 "" 
{TEXT -1 53 "Calculated Ndd(dn,dn) for desitter_sf (.001000 sec.) " }}
{PARA 6 "" 1 "" {TEXT -1 55 "Calculated K(dn,dn,cdn) for desitter_sf (
.007000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 53 "Calculated Ni(up,cdn) f
or desitter_sf (.003000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 51 "Calcula
ted K(dn,up) for desitter_sf (.002000 sec.) " }}{PARA 6 "" 1 "" {TEXT 
-1 51 "Calculated T(up,dn) for desitter_sf (.007000 sec.) " }}{PARA 6 
"" 1 "" {TEXT -1 55 "Calculated derpK(dn,dn) for desitter_sf (.065000 \+
sec.) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"$\"G!\"$" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "gralter(derpK(dn,dn),factor
,tringsin,sqrt,simplify);" }}{PARA 6 "" 1 "" {TEXT -1 48 "Component si
mplification of a GRTensorII object:" }}{PARA 6 "" 1 "" {TEXT -1 1 " \+
" }}{PARA 6 "" 1 "" {TEXT -1 56 "Applying routine `simplify[sqrt]` to \+
object derpK(dn,dn)" }}{PARA 6 "" 1 "" {TEXT -1 48 "Applying routine s
implify to object derpK(dn,dn)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*C
PU~Time~G$\"%UW!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "grdi
splay(derpK(dn,dn));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?For~the~desi
tter_sf~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%-derpK(dn,dn)G
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&derpKG6$%#dnGF&" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#/*&&%&derpKG6#%\"rG\"\"\"&%!GF'F)%K~15883~words.~E
xceeds~grOptionDisplayLimitG" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/*&&%&
derpKG6#%&thetaG\"\"\"&%!G6#%\"rGF),,*&F-F)-%%diffG6$-%\"NG6&%\"tGF-F(
%$phiGF(F)!\"\"*&)F-\"\"#\"\"\"-F16%F3F-F(F)F8*(F3F)-F16$-%$psiGF5F(F)
-F16$FBF-F)F8*&-%#KaGF5F)-F16$-%#N1GF5F(F)F)*&-%#KbGF5F)-F16$-%#N2GF5F
-F)F)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/*&&%&derpKG6#%$phiG\"\"\"&%!
G6#%\"rGF),0*&F-F)-%%diffG6$-%\"NG6&%\"tGF-%&thetaGF(F(F)!\"\"*(F-\"\"
\"F0F:)-%$cosG6#F7\"\"#F:F)*&)F-F?F:-F16%F3F(F-F)F8*(FAF:FBF:F;F:F)*(F
3F)-F16$-%$psiGF5F(F)-F16$FHF-F)F8*&-%#KaGF5F)-F16$-%#N1GF5F(F)F)*&-%#
KcGF5F)-F16$-%#N3GF5F-F)F)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/*&&%&de
rpKG6#%\"rG\"\"\"&%!G6#%&thetaGF),,*(%\"aGF))%\"tG#\"\"%\"\"$\"\"\"-%%
diffG6%-%\"NG6&F2F(F-%$phiGF(F-F)!\"\"*&F(F)-F86$F:F-F)F)*(F:F)-F86$-%
$psiGF<F-F)-F86$FEF(F)F>*&-%#KaGF<F)-F86$-%#N1GF<F-F)F)*&-%#KbGF<F)-F8
6$-%#N2GF<F(F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&derpKG6#%&th
etaG\"\"\"&%!GF'F)%K~16289~words.~Exceeds~grOptionDisplayLimitG" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#/*&&%&derpKG6#%$phiG\"\"\"&%!G6#%&thet
aGF),.**)%\"rG\"\"#\"\"\"-%$sinGF,F)-%%diffG6$-%\"NG6&%\"tGF1F-F(F(F)-
%$cosGF,F)!\"\"*&F0F3-F76%F9F(F-F)F?*(F0F3FAF3)F=F2F3F)*(F9F)-F76$-%$p
siGF;F(F)-F76$FHF-F)F?*&-%#KbGF;F)-F76$-%#N2GF;F(F)F)*&-%#KcGF;F)-F76$
-%#N3GF;F-F)F)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/*&&%&derpKG6#%\"rG
\"\"\"&%!G6#%$phiGF),.*(%\"aGF))%\"tG#\"\"%\"\"$\"\"\"-%%diffG6%-%\"NG
6&F2F(%&thetaGF-F-F(F)!\"\"*&F(F)-F86$F:F-F)F)*(F(F6F@F6)-%$cosG6#F=\"
\"#F6F>*(F:F)-F86$-%$psiGF<F-F)-F86$FKF(F)F>*&-%#KaGF<F)-F86$-%#N1GF<F
-F)F)*&-%#KcGF<F)-F86$-%#N3GF<F(F)F)" }}{PARA 12 "" 1 "" {XPPMATH 20 "
6#/*&&%&derpKG6#%&thetaG\"\"\"&%!G6#%$phiGF),,*&)%\"rG\"\"#\"\"\"-%%di
ffG6%-%\"NG6&%\"tGF1F(F-F-F(F)!\"\"**F0F3-%$sinGF'F)-F56$F7F-F)-%$cosG
F'F)F)*(F7F)-F56$-%$psiGF9F-F)-F56$FFF(F)F;*&-%#KbGF9F)-F56$-%#N2GF9F-
F)F)*&-%#KcGF9F)-F56$-%#N3GF9F(F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#/*&&%&derpKG6#%$phiG\"\"\"&%!GF'F)%K~23789~words.~Exceeds~grOptionDis
playLimitG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "grcalc(T00);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "grdisplay(T00);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#%?For~the~desitter_sf~spacetime:G" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#%$T00G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%$T00G%J~6
887~words.~Exceeds~grOptionDisplayLimitG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "grcalc(T(dn,dn));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
/%*CPU~Time~G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "grdis
play(T(dn,dn));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?For~the~desitter_
sf~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%)T(dn,dn)G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"TG6$%#dnGF&" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#/*&&%\"TG6#%\"rG\"\"\"&%!GF'F),$*&,>**)-%%diffG6$-%$psi
G6&%\"tGF(%&thetaG%$phiGF(\"\"#\"\"\")-%\"NGF6F:F;)F(F:F;)-%$sinG6#F8F
:F;F)*,)-F26$F4F7F:F;%\"aGF))F7#\"\"%\"\"$F;F?F;F@F;F)*0)%\"mGF:F;)F4F
:F;F<F;FHF;FIF;F?F;F@F;!\"\"*0-%#N1GF6F)FFF)F1F)FHF;FIF;F?F;F@F;!\"#*.
F0F;)FSF:F;FHF;FIF;F?F;F@F;F)*2F1F;-F26$F4F8F)FSF;-%#N2GF6F)FHF;FIF;F?
F;F@F;F:*2F1F;-F26$F4F9F)FSF;-%#N3GF6F)FHF;FIF;F?F;F@F;F:*0FenF;FFF;FY
F;FHF;FIF;F?F;F@F;FU*,)FYF:F;F<F;FHF;FIF;F@F;FQ*.F^oF;)FenF:F;FHF;FIF;
F?F;F@F;F)*2FYF;FhnF;FenF;FjnF;FHF;FIF;F?F;F@F;F:*0FjnF;FFF;FhnF;FHF;F
IF;F?F;F@F;FU**)FhnF:F;F<F;FHF;FIF;FQ*.FdoF;)FjnF:F;FHF;FIF;F?F;F@F;F)
F;*()F=\"\"#F;)F(\"\"#F;)FA\"\"#F;!\"\"#F)F:" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/*&&%\"TG6#%&thetaG\"\"\"&%!G6#%\"rGF)*&-%%diffG6$-%$ps
iG6&%\"tGF-F(%$phiGF(F)-F06$F2F-F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
/*&&%\"TG6#%$phiG\"\"\"&%!G6#%\"rGF)*&-%%diffG6$-%$psiG6&%\"tGF-%&thet
aGF(F(F)-F06$F2F-F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%\"TG6#%\"r
G\"\"\"&%!G6#%&thetaGF)*&-%%diffG6$-%$psiG6&%\"tGF(F-%$phiGF-F)-F06$F2
F(F)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/*&&%\"TG6#%&thetaG\"\"\"&%!GF
'F),$*&,>*,)-%%diffG6$-%$psiG6&%\"tG%\"rGF(%$phiGF(\"\"#\"\"\")-%\"NGF
6F:F;%\"aGF))F7#\"\"%\"\"$F;)-%$sinGF'F:F;F)*,)-F26$F4F7F:F;F?F;F@F;)F
8F:F;FDF;F)*0)%\"mGF:F;)F4F:F;F<F;F?F;F@F;FKF;FDF;!\"\"*0-%#N1GF6F)FIF
)-F26$F4F8F)F?F;F@F;FKF;FDF;!\"#**)FTF:F;F<F;FKF;FDF;FP*.FXF;)FRF:F;F?
F;F@F;FKF;FDF;F)*2FTF;F1F)FRF;-%#N2GF6F)F?F;F@F;FKF;FDF;F:*2FTF;-F26$F
4F9F)FRF;-%#N3GF6F)F?F;F@F;FKF;FDF;F:*0FfnF;FIF;F1F;F?F;F@F;FKF;FDF;FV
*.F0F;)FfnF:F;F?F;F@F;FKF;FDF;F)*2F1F;FinF;FfnF;F[oF;F?F;F@F;FKF;FDF;F
:*0F[oF;FIF;FinF;F?F;F@F;FKF;FDF;FV**)FinF:F;F<F;F?F;F@F;FP*.FcoF;)F[o
F:F;F?F;F@F;FKF;FDF;F)F;**)F=\"\"#F;F?\"\"\")F7#\"\"%FCF;)FE\"\"#F;!\"
\"#F)F:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%\"TG6#%$phiG\"\"\"&%!G
6#%&thetaGF)*&-%%diffG6$-%$psiG6&%\"tG%\"rGF-F(F(F)-F06$F2F-F)" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%\"TG6#%\"rG\"\"\"&%!G6#%$phiGF)*&
-%%diffG6$-%$psiG6&%\"tGF(%&thetaGF-F-F)-F06$F2F(F)" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#/*&&%\"TG6#%&thetaG\"\"\"&%!G6#%$phiGF)*&-%%diffG6$-%
$psiG6&%\"tG%\"rGF(F-F-F)-F06$F2F(F)" }}{PARA 12 "" 1 "" {XPPMATH 20 "
6#/*&&%\"TG6#%$phiG\"\"\"&%!GF'F),$*&,>**)-%%diffG6$-%$psiG6&%\"tG%\"r
G%&thetaGF(F(\"\"#\"\"\")-%\"NGF6F:F;%\"aGF))F7#\"\"%\"\"$F;F)*,)-F26$
F4F7F:F;F?F;F@F;)F8F:F;)-%$sinG6#F9F:F;F)*0)%\"mGF:F;)F4F:F;F<F;F?F;F@
F;FHF;FIF;!\"\"*0-%#N1GF6F)FFF)-F26$F4F8F)F?F;F@F;FHF;FIF;!\"#**)FUF:F
;F<F;FHF;FIF;FQ*.FYF;)FSF:F;F?F;F@F;FHF;FIF;F)*2FUF;-F26$F4F9F)FSF;-%#
N2GF6F)F?F;F@F;FHF;FIF;F:*2FUF;F1F)FSF;-%#N3GF6F)F?F;F@F;FHF;FIF;F:*0F
inF;FFF;FgnF;F?F;F@F;FHF;FIF;FW*,)FgnF:F;F<F;F?F;F@F;FIF;FQ*.F`oF;)Fin
F:F;F?F;F@F;FHF;FIF;F)*2FgnF;F1F;FinF;F\\oF;F?F;F@F;FHF;FIF;F:*0F\\oF;
FFF;F1F;F?F;F@F;FHF;FIF;FW*.F0F;)F\\oF:F;F?F;F@F;FHF;FIF;F)F;*()F=\"\"
#F;F?\"\"\")F7#\"\"%FCF;!\"\"#F)F:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "grcalc(T0(dn));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%
*CPU~Time~G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "grdispl
ay(T0(dn));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?For~the~desitter_sf~s
pacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'T0(dn)G" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#-%#T0G6#%#dnG" }}{PARA 12 "" 1 "" {XPPMATH 20 "6
#/&%#T0G6#%\"rG*&,@*,-%%diffG6$-%$psiG6&%\"tGF'%&thetaG%$phiGF1\"\"\"-
F,6$F.F'F4)-%\"NGF0\"\"#\"\"\")F'F:F;)-%$sinG6#F2F:F;F4*.-%#N1GF0F4)F+
F:F;%\"aGF4)F1#\"\"%\"\"$F;F<F;F=F;F4*2FBF;)%\"mGF:F;)F.F:F;F7F;FEF;FF
F;F<F;F=F;!\"\"*0)FBF:F;F+F;F5F;FEF;FFF;F<F;F=F;!\"#*,FBF;)F5F:F;F7F;F
<F;F=F;FN*.FSF;)FBFIF;FEF;FFF;F<F;F=F;F4*2F5F;-F,6$F.F2F4FPF;-%#N2GF0F
4FEF;FFF;F<F;F=F;F:*2F5F;-F,6$F.F3F4FPF;-%#N3GF0F4FEF;FFF;F<F;F=F;F:*2
FBF;FYF;F+F;FWF;FEF;FFF;F<F;F=F;FQ*.FBF;)FWF:F;F7F;FEF;FFF;F=F;FN*0FBF
;F\\oF;)FYF:F;FEF;FFF;F<F;F=F;F4*4FBF;FWF;FfnF;FYF;FhnF;FEF;FFF;F<F;F=
F;F:*2FBF;FhnF;F+F;FfnF;FEF;FFF;F<F;F=F;FQ*,FBF;)FfnF:F;F7F;FEF;FFF;FN
*0FBF;FboF;)FhnF:F;FEF;FFF;F<F;F=F;F4F;*()F8\"\"#F;)F'\"\"#F;)F>\"\"#F
;!\"\"" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/&%#T0G6#%&thetaG*&,@*.-%%di
ffG6$-%$psiG6&%\"tG%\"rGF'%$phiGF1\"\"\"-F,6$F.F'F4)-%\"NGF0\"\"#\"\"
\"%\"aGF4)F1#\"\"%\"\"$F;)-%$sinGF&F:F;F4*.-%#N2GF0F4)F+F:F;F<F;F=F;)F
2F:F;FAF;F4*2FEF;)%\"mGF:F;)F.F:F;F7F;F<F;F=F;FHF;FAF;!\"\"*2FEF;-%#N1
GF0F4F+F;-F,6$F.F2F4F<F;F=F;FHF;FAF;!\"#*,FEF;)FQF:F;F7F;FHF;FAF;FM*0F
EF;FUF;)FOF:F;F<F;F=F;FHF;FAF;F4*2FQF;F5F;FOF;)FEF:F;F<F;F=F;FHF;FAF;F
:*4FEF;FQF;-F,6$F.F3F4FOF;-%#N3GF0F4F<F;F=F;FHF;FAF;F:*0FYF;F+F;F5F;F<
F;F=F;FHF;FAF;FS*.FEF;)F5F:F;F7F;F<F;F=F;FAF;FM*.F[oF;)FEF@F;F<F;F=F;F
HF;FAF;F4*2F5F;FenF;FYF;FgnF;F<F;F=F;FHF;FAF;F:*2FEF;FgnF;F+F;FenF;F<F
;F=F;FHF;FAF;FS*,FEF;)FenF:F;F7F;F<F;F=F;FM*0FEF;FaoF;)FgnF:F;F<F;F=F;
FHF;FAF;F4F;**)F8\"\"#F;F<\"\"\")F1#\"\"%F@F;)FB\"\"#F;!\"\"" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#/&%#T0G6#%$phiG*&,@*,-%%diffG6$-%$psiG6&%\"t
G%\"rG%&thetaGF'F1\"\"\"-F,6$F.F'F4)-%\"NGF0\"\"#\"\"\"%\"aGF4)F1#\"\"
%\"\"$F;F4*.-%#N3GF0F4)F+F:F;F<F;F=F;)F2F:F;)-%$sinG6#F3F:F;F4*2FBF;)%
\"mGF:F;)F.F:F;F7F;F<F;F=F;FEF;FFF;!\"\"*2FBF;-%#N1GF0F4F+F;-F,6$F.F2F
4F<F;F=F;FEF;FFF;!\"#*,FBF;)FRF:F;F7F;FEF;FFF;FN*0FBF;FVF;)FPF:F;F<F;F
=F;FEF;FFF;F4*4FBF;FRF;-F,6$F.F3F4FPF;-%#N2GF0F4F<F;F=F;FEF;FFF;F:*2FR
F;F5F;FPF;)FBF:F;F<F;F=F;FEF;FFF;F:*2FBF;FfnF;F+F;FZF;F<F;F=F;FEF;FFF;
FT*.FBF;)FZF:F;F7F;F<F;F=F;FFF;FN*0FBF;F\\oF;)FfnF:F;F<F;F=F;FEF;FFF;F
4*2FZF;F5F;FfnF;FinF;F<F;F=F;FEF;FFF;F:*0FinF;F+F;F5F;F<F;F=F;FEF;FFF;
FT*,FBF;)F5F:F;F7F;F<F;F=F;FN*.FboF;)FBF@F;F<F;F=F;FEF;FFF;F4F;*()F8\"
\"#F;F<\"\"\")F1#\"\"%F@F;!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
12 "Shift zero !" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "N1(t,r,
theta,phi):=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#N1G6&%\"tG%\"rG%
&thetaG%$phiG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "N2(t,
r,theta,phi):=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#N2G6&%\"tG%\"r
G%&thetaG%$phiG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "N3(
t,r,theta,phi):=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#N3G6&%\"tG%
\"rG%&thetaG%$phiG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "
grdisplay(T00);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?For~the~desitter_
sf~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%$T00G" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#/%$T00G,$*&,,*,)-%\"NG6&%\"tG%\"rG%&thetaG%$phiG
\"\"%\"\"\")-%%diffG6$-%$psiGF,F/\"\"#F2%\"aG\"\"\")F-#F1\"\"$F2)-%$si
nG6#F/F9F2F;*0F)F2)%\"mGF9F2)F7F9F2F:F2F<F2)F.F9F2F?F2F;**F)F2)-F56$F7
F0F9F2F:F2F<F2F;**F)F2)-F56$F7F.F9F2FGF2F?F2F;*.)-F56$F7F-F9F2)F*F9F2F
:F2F<F2FGF2F?F2F;F2*,)F*\"\"#F2F:\"\"\")F-#\"\"%F>F2)F.\"\"#F2)F@\"\"#
F2!\"\"#F;F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "grdisplay(T
(dn,dn));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?For~the~desitter_sf~spa
cetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%)T(dn,dn)G" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#-%\"TG6$%#dnGF&" }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#/*&&%\"TG6#%\"rG\"\"\"&%!GF'F),$*&,,**)-%%diffG6$-%$psiG6&%\"tGF(%&
thetaG%$phiGF(\"\"#\"\"\")-%\"NGF6F:F;)F(F:F;)-%$sinG6#F8F:F;F)*,)-F26
$F4F7F:F;%\"aGF))F7#\"\"%\"\"$F;F?F;F@F;F)*0)%\"mGF:F;)F4F:F;F<F;FHF;F
IF;F?F;F@F;!\"\"*,)-F26$F4F8F:F;F<F;FHF;FIF;F@F;FQ**)-F26$F4F9F:F;F<F;
FHF;FIF;FQF;*()F=\"\"#F;)F(\"\"#F;)FA\"\"#F;!\"\"#F)F:" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#/*&&%\"TG6#%&thetaG\"\"\"&%!G6#%\"rGF)*&-%%diffG6$
-%$psiG6&%\"tGF-F(%$phiGF(F)-F06$F2F-F)" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/*&&%\"TG6#%$phiG\"\"\"&%!G6#%\"rGF)*&-%%diffG6$-%$psiG6&%\"tGF-
%&thetaGF(F(F)-F06$F2F-F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%\"TG
6#%\"rG\"\"\"&%!G6#%&thetaGF)*&-%%diffG6$-%$psiG6&%\"tGF(F-%$phiGF-F)-
F06$F2F(F)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/*&&%\"TG6#%&thetaG\"\"
\"&%!GF'F),$*&,,*,)-%%diffG6$-%$psiG6&%\"tG%\"rGF(%$phiGF(\"\"#\"\"\")
-%\"NGF6F:F;%\"aGF))F7#\"\"%\"\"$F;)-%$sinGF'F:F;F)*,)-F26$F4F7F:F;F?F
;F@F;)F8F:F;FDF;F)*0)%\"mGF:F;)F4F:F;F<F;F?F;F@F;FKF;FDF;!\"\"**)-F26$
F4F8F:F;F<F;FKF;FDF;FP**)-F26$F4F9F:F;F<F;F?F;F@F;FPF;**)F=\"\"#F;F?\"
\"\")F7#\"\"%FCF;)FE\"\"#F;!\"\"#F)F:" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#/*&&%\"TG6#%$phiG\"\"\"&%!G6#%&thetaGF)*&-%%diffG6$-%$psiG6&%\"tG%
\"rGF-F(F(F)-F06$F2F-F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%\"TG6#
%\"rG\"\"\"&%!G6#%$phiGF)*&-%%diffG6$-%$psiG6&%\"tGF(%&thetaGF-F-F)-F0
6$F2F(F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%\"TG6#%&thetaG\"\"\"&
%!G6#%$phiGF)*&-%%diffG6$-%$psiG6&%\"tG%\"rGF(F-F-F)-F06$F2F(F)" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#/*&&%\"TG6#%$phiG\"\"\"&%!GF'F),$*&,,*
*)-%%diffG6$-%$psiG6&%\"tG%\"rG%&thetaGF(F(\"\"#\"\"\")-%\"NGF6F:F;%\"
aGF))F7#\"\"%\"\"$F;F)*,)-F26$F4F7F:F;F?F;F@F;)F8F:F;)-%$sinG6#F9F:F;F
)*0)%\"mGF:F;)F4F:F;F<F;F?F;F@F;FHF;FIF;!\"\"**)-F26$F4F8F:F;F<F;FHF;F
IF;FQ*,)-F26$F4F9F:F;F<F;F?F;F@F;FIF;FQF;*()F=\"\"#F;F?\"\"\")F7#\"\"%
FCF;!\"\"#F)F:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "grdisplay
(T0(dn));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%?For~the~desitter_sf~spa
cetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'T0(dn)G" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#-%#T0G6#%#dnG" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/
&%#T0G6#%\"aG-%'vectorG6#7%*&-%%diffG6$-%$psiG6&%\"tG%\"rG%&thetaG%$ph
iGF3\"\"\"-F.6$F0F4F7*&F-\"\"\"-F.6$F0F5F7*&F-F;-F.6$F0F6F7" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "grcalc(derge(dn,dn));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"\"\"!\"$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "grdisplay(derge(dn,dn));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%?For~the~desitter_sf~spacetime:G" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%-derge(dn,dn)G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%&dergeG6$%#dnGF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/
*&&%&dergeG6#%\"aG\"\"\"&%!G6#%\"bGF)-%'matrixG6#7%7%,$*&-%\"NG6&%\"tG
%\"rG%&thetaG%$phiGF)-%#KaGF7F)!\"#\"\"!F?7%F?,$*&F5\"\"\"-%#KbGF7F)F>
F?7%F?F?,$*&F5FC-%#KcGF7F)F>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 36 "grcomponent(derpK(dn,dn),[phi,phi]);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,$*&,do*()-%\"NG6&
%\"tG%\"rG%&thetaG%$phiG\"\"%\"\"\")F,\"\"#F0)-%$cosG6#F-F/F0!\"%**F'F
0)F,F/F0)-%%diffG6$-%$psiGF*F,F2F0)F4F2F0!\"#*(F'F0F1F0F@F0\"\")**F'F0
F1F0%\"aG\"\"\")F+#F/\"\"$F0F/*.-F<6$F(F,FF)F,FIF0)F(FIF0FEF0FGF0F@F0F
C*,FKF0FMF0FNF0FEF0FGF0F7*0F'F0F9F0)%\"mGF2F0)F>F2F0FEF0FGF0F@F0F2*.F'
F0F9F0FQF0FSF0FEF0FGF0!\"\"*.)F(F2F0F9F0)-F<6$F>F+F2F0FEF0FGF0F@F0FA*,
FWF0F9F0FXF0FEF0FGF0FF*,F'F0F1F0FEF0FGF0F@F0!\")*,F9F0%$T00GFFFWF0FEF0
FGF0F2*.F9F0FinF0FWF0FEF0FGF0F@F0F7*,F'F0F1F0)-F<6$F>F-F2F0FEF0FGF0FF*
.F'F0F1F0F\\oF0FEF0FGF0F@F0FA*&F'F0F1F0F7*.F9F0-F<6$F(-%\"$G6$F.F2FFFN
F0FEF0FGF0F3F0F7**F'F0F9F0F:F0F3F0FF*.F9F0FboF0FNF0FEF0FGF0F@F0FC*,F9F
0FboF0FNF0FEF0FGF0F7*(F'F0F9F0F:F0FF*.FKF0FMF0FNF0FEF0FGF0F3F0F7**F'F0
-%#KcGF*FF-%#KaGF*FFF1F0F/*0F9F0-F<6$F(F-FF)F4FIF0FNF0FEF0FGF0-%$sinGF
6FFF/*0F9F0FbpF0F4FFFNF0FEF0FGF0FepF0F7*,F'F0F1F0FEF0FGF0F3F0F/*,F'F0F
]pF0F_pF0F1F0F@F0F7*.F'F0F]pF0-%#KbGF*FFFEF0FGF0F@F0F7*,F'F0F]pF0F[qF0
FEF0FGF0F/*.F'F0F1F0)-F<6$F>F.F2F0FEF0FGF0F@F0FI*0F'F0F9F0FQF0FSF0FEF0
FGF0F3F0FU*.FWF0F9F0FXF0FEF0FGF0F3F0FF*.F'F0F1F0F\\oF0FEF0FGF0F3F0FF*,
F'F0F1F0F_qF0FEF0FGF0!\"$*.F9F0FinF0FWF0FEF0FGF0F3F0F2**F'F0)F]pF2F0FE
F0FGF0F7F0*,)F(\"\"$F0)F,\"\"#F0FE\"\"\")F+#\"\"%FIF0,&FUFF*$F@F0FF\"
\"\"!\"\"#FUF/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "Lapse one !" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "N(t,r,theta,phi):=1;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"NG6&%\"tG%\"rG%&thetaG%$phiG\"\"
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "grdisplay(ha0);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%?For~the~desitter_sf~spacetime:G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%$ha0G" }}{PARA 12 "" 1 "" {XPPMATH 
20 "6#/%$ha0G,6*&\"\"\"F'*$)%\"rG\"\"#F'!\"\"\"\"#*$)-%%diffG6$-%$psiG
6&%\"tGF*%&thetaG%$phiGF6F-F'\"\"\"*&*$)-F16$F3F8F-F'F'*&)F*\"\"#F')-%
$sinG6#F7\"\"#F'F,F9*&*&-%#KaGF5F9-%#KcGF5F9F'**)F*\"\"#F'%\"aG\"\"\")
F6#\"\"%\"\"$F')FC\"\"#F'F,F-*&*&-%#KbGF5F9FKF'F'*&)F*\"\"%F')FC\"\"#F
'F,F-*&F'F'*()F*\"\"#F'FP\"\"\")F6#\"\"%FUF'F,!\"#*&*&FIF'FZF'F'*()F*
\"\"#F'FP\"\"\")F6#\"\"%FUF'F,F-*&*$)-F16$F3F*F-F'F'*&FP\"\"\")F6#\"\"
%FUF'F,F9*&*$)-F16$F3F7F-F'F'*$)F*\"\"#F'F,F9*&)%\"mGF-F')F3F-F'F9" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "grdisplay(ha(dn));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%?For~the~desitter_sf~spacetime:G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%'ha(dn)G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%#haG6#%#dnG" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/&%#ha
G6#%\"rG,.*&-%#KaG6&%\"tGF'%&thetaG%$phiG\"\"\"*(F'\"\"\"%\"aG\"\"\")F
-#\"\"%\"\"$F0!\"\"\"\"#*&-%#KcGF,F0*&)F'\"\"$F0)-%$sinG6#F.\"\"#F0F9
\"\"\"*&-%#KbGF,F0*$)F'\"\"$F0F9FF*&-%%diffG6$FHF'F0*$)F'\"\"#F0F9!\"
\"*&-FO6$F<F'F0*&)F'\"\"#F0)FB\"\"#F0F9FT*&-FO6$-%$psiGF,F-FF-FO6$FjnF
'FFFF" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/&%#haG6#%&thetaG,,*&-%%diffG
6$-%#KaG6&%\"tG%\"rGF'%$phiGF'\"\"\"*&%\"aG\"\"\")F0#\"\"%\"\"$F3!\"\"
!\"\"*&-F+6$-%$psiGF/F0\"\"\"-F+6$F@F'FBFB*&*&-%#KbGF/FB-%$cosGF&FBF3*
&)F1\"\"#F3-%$sinGF&\"\"\"F;FB*&*&-%#KcGF/FBFIF3F3*&)F1\"\"#F3)FN\"\"$
F3F;FB*&-F+6$FSF'F3*&)F1\"\"#F3)FN\"\"#F3F;F<" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/&%#haG6#%$phiG,(*&-%%diffG6$-%#KaG6&%\"tG%\"rG%&thetaG
F'F'\"\"\"*&%\"aG\"\"\")F0#\"\"%\"\"$F3!\"\"!\"\"*&-F+6$-%$psiGF/F0\"
\"\"-F+6$F@F'FBFB*&-F+6$-%#KbGF/F'F3*$)F1\"\"#F3F;F<" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 28 "gralter(ha0,trigsin,expand);" }}{PARA 6 "
" 1 "" {TEXT -1 48 "Component simplification of a GRTensorII object:" 
}}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 50 "Applyi
ng routine `simplify[trigsin]` to object ha0" }}{PARA 6 "" 1 "" {TEXT 
-1 37 "Applying routine expand to object ha0" }}{PARA 11 "" 1 "" 
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