> restart:

Standard Worksheet SSSPF

P-S2

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(pstwo);

Physical parameters

> grcalc(Iso,rho,p,mass):

> gralter(_,1,7):

Component simplification of a GRTensorII object:

Applying routine simplify to object Iso

Applying routine simplify to object rho

Applying routine simplify to object p

Applying routine simplify 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(_);

Perssure plots

> pj:=subs(c = alpha-1+sqrt(alpha^2-2*alpha),Delta = (alpha-1+sqrt((alpha-2)*alpha)+n)/(n*alpha-n+n*sqrt((alpha-2)*alpha)+1),n=2,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 P-S2 n=2");

Energy density plots

> rhoj:=subs(c = alpha-1+sqrt(alpha^2-2*alpha),Delta = (alpha-1+sqrt((alpha-2)*alpha)+n)/(n*alpha-n+n*sqrt((alpha-2)*alpha)+1),n=2,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 P-S2 n=2");

Mass plots

> mj:=subs(c = alpha-1+sqrt(alpha^2-2*alpha),Delta = (alpha-1+sqrt((alpha-2)*alpha)+n)/(n*alpha-n+n*sqrt((alpha-2)*alpha)+1),n=2,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 P-S2 n=2");

Trapping

Potential impac parameter

> B:=sqrt(grcomponent(g(dn,dn),[theta,theta]))/sqrt(-grcomponent(g(dn,dn),[t,t])):

> Bj:=subs(c = alpha-1+sqrt(alpha^2-2*alpha),Delta = (alpha-1+sqrt((alpha-2)*alpha)+n)/(n*alpha-n+n*sqrt((alpha-2)*alpha)+1),n=2,R=1,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 P-S2 n=2");

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(c = alpha-1+sqrt(alpha^2-2*alpha),Delta = (alpha-1+sqrt((alpha-2)*alpha)+n)/(n*alpha-n+n*sqrt((alpha-2)*alpha)+1),n=2,R=1,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 P-S2 n=2");

V:=sqrt(dp/dr/drho/dr)

> vs:=sqrt(diff(grcomponent(p,[]),xi)/(diff(grcomponent(rho,[]),xi))):

> vsj:=subs(c = alpha-1+sqrt(alpha^2-2*alpha),Delta = (alpha-1+sqrt((alpha-2)*alpha)+n)/(n*alpha-n+n*sqrt((alpha-2)*alpha)+1),n=2,R=1,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,vsj):

> plot([vs1,vs2,vs3,vs4],xi=0..1,color=[red,green,blue,black],title="V P-S2 n=2");

>