> restart:
Standard Worksheet SSSPF
GOLD III
Physical quatities are defined in the initialization file
> grts();
Created definition for G(up,dn)
Created definition for rho
Created definition for Iso
Created definition for p
Created definition for gthetatheta
Created definition for R(dn,dn,up,up)
Created definition for mass
> qload(goldthree);
Physical parameters
> grcalc(Iso,rho,p,mass):
> gralter(_,6,7):
Component simplification of a GRTensorII object:
Applying routine expand to object Iso
Applying routine expand to object rho
Applying routine expand to object p
Applying routine expand to object mass
Applying routine factor to object Iso
Applying routine factor to object rho
Applying routine factor to object p
Applying routine factor to object mass
> grdisplay(_);
Junction conditions
> c1:=ln(sqrt(alpha*(alpha-2))+alpha-1+sqrt(2*alpha^2-4*alpha+2*sqrt(alpha*(alpha-2))*alpha-2*sqrt(alpha*(alpha-2))));
> k1:=1/8/alpha*(2*alpha-2*sqrt(alpha^2-2*alpha))*(1+(sqrt(alpha*(alpha-2))+alpha-1+sqrt(2*alpha^2-4*alpha+2*sqrt(alpha*(alpha-2))*alpha-2*sqrt(alpha*(alpha-2))))^2)*(sqrt(alpha*(alpha-2))+alpha+sqrt(2*alpha^2-4*alpha+2*sqrt(alpha*(alpha-2))*alpha-2*sqrt(alpha*(alpha-2))))/(sqrt(alpha*(alpha-2))+alpha-1+sqrt(2*alpha^2-4*alpha+2*sqrt(alpha*(alpha-2))*alpha-2*sqrt(alpha*(alpha-2))))/(-2+sqrt(alpha*(alpha-2))+alpha+sqrt(2*alpha^2-4*alpha+2*sqrt(alpha*(alpha-2))*alpha-2*sqrt(alpha*(alpha-2))));
Perssure plots
> pj:=subs(c=c1,k=k1,grcomponent(p,[])):
> p1:=subs(R=1,alpha=6,pj):
> p2:=subs(R=1,alpha=5,pj):
> p3:=subs(R=1,alpha=4,pj):
> p4:=subs(R=1,alpha=3,pj):
> plot([p1,p2,p3,p4],xi=0..1,color=[red,green,blue,black],title="Pressure Gold III");
![[Maple Plot]](imagesgoldiii/goldiii40.gif)
Energy density plots
> rhoj:=subs(c=c1,k=k1,grcomponent(rho,[])):
> rho1:=subs(R=1,alpha=6,rhoj):
> rho2:=subs(R=1,alpha=5,rhoj):
> rho3:=subs(R=1,alpha=4,rhoj):
> rho4:=subs(R=1,alpha=3,rhoj):
> plot([rho1,rho2,rho3,rho4],xi=0..1,color=[red,green,blue,black],title="Energy Density Gold III");
![[Maple Plot]](imagesgoldiii/goldiii41.gif)
Mass plots
> mj:=subs(c=c1,k=k1,grcomponent(mass,[])):
> mj1:=subs(R=1,alpha=6,mj):
> mj2:=subs(R=1,alpha=5,mj):
> mj3:=subs(R=1,alpha=4,mj):
> mj4:=subs(R=1,alpha=3,mj):
> plot([mj1,mj2,mj3,mj4],xi=0..1,color=[red,green,blue,black],title="Mass Gold III");
![[Maple Plot]](imagesgoldiii/goldiii42.gif)
Trapping
Potential impac parameter
> B:=radsimp(sqrt(grcomponent(g(dn,dn),[theta,theta]))/sqrt(-grcomponent(g(dn,dn),[t,t])));
> Bj:=subs(R=1,c=c1,k=k1,B):
> B1:=subs(alpha=6,Bj):
> B2:=subs(alpha=5,Bj):
> B3:=subs(alpha=4,Bj):
> B4:=subs(alpha=3,Bj):
> plot([B1,B2,B3,B4],xi=0..1,color=[red,green,blue,black],title="Trapping Gold III");
![[Maple Plot]](imagesgoldiii/goldiii44.gif)
w - modes
Potential
> V:=1/((Bj^2))*(6+4*Pi*xi^2*R^2*(grcomponent(rho,[])-grcomponent(p,[]))-6*grcomponent(mass,[])/(xi*R)):
> Vj:=subs(R=1,c=c1,k=k1,V):
> V1:=subs(alpha=6,Vj):
> V2:=subs(alpha=5,Vj):
> V3:=subs(alpha=4,Vj):
> V4:=subs(alpha=3,Vj):
> plot([V1,V2,V3,V4],xi=0.1..1.0,color=[red,green,blue,black],title="w - modes Gold III");
![[Maple Plot]](imagesgoldiii/goldiii45.gif)
V:=sqrt(dp/dr/drho/dr)
> vs:=sqrt(diff(grcomponent(p,[]),xi)/(diff(grcomponent(rho,[]),xi))):
> vsj:=subs(R=1,c=c1,k=k1,f=f1,vs):
> vs1:=subs(R=1,alpha=6,vsj):
> vs2:=subs(R=1,alpha=5,vsj):
> vs3:=subs(R=1,alpha=4,vsj):
> vs4:=subs(R=1,alpha=3.75,vsj):
> plot([vs1,vs2,vs3,vs4],xi=0..1,color=[red,green,blue,black],title="V Gold III");
![[Maple Plot]](imagesgoldiii/goldiii46.gif)
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