> restart:

Standard Worksheet SSSPF

Tolman VII

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(tviia);

Physical parameters

> grcalcd(Iso,rho,p,mass);

Junction conditions

> A:=1/3*3^(3/4)*2^(1/4)*(alpha*(5*gamma-3))^(1/4):

> K:= 1/10*10^(1/2)*(alpha*(5*gamma-3))^(1/2)/gamma^(1/2):

> C:=-1/6*(-sqrt(gamma)*sqrt(3)*sqrt(2)*sqrt(alpha*(5*gamma-3))*sqrt(alpha*(alpha-2)*gamma)+5*alpha*gamma^2-6*alpha*gamma)*3^(1/2)*2^(1/2)/alpha/exp(2*arctan(alpha*gamma^(1/2)*(alpha-2)*3^(1/2)*2^(1/2)/(alpha*(alpha-2)*gamma)^(1/2)/(alpha*(5*gamma-3))^(1/2)))/(alpha*(5*gamma-3))^(1/2)/gamma:

Perssure plots (gamma=1)

> pj:=subs(gamma=1,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 Tolman VII");

Energy density plots

> rhoj:=subs(gamma=1,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 Tolman VII");

Mass plots

> mj:=subs(gamma=1,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 Tolman VII");

Trapping

Potential impac parameter

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

> Bj:=subs(R=1,gamma=1,B):

> B1:=subs(alpha=3.17,Bj):

> B2:=subs(alpha=3.18,Bj):

> B3:=subs(alpha=3.19,Bj):

> B4:=subs(alpha=3.2,Bj):

> plot([B1,B2,B3,B4],xi=0.85..1,color=[red,green,blue,black],title="Trapping Tolman VII");

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,gamma=1,V):

> V1:=subs(alpha=2.8,Vj):

> V2:=subs(alpha=2.9,Vj):

> V3:=subs(alpha=3.0,Vj):

> V4:=subs(alpha=3.02,Vj):

> plot([V1,V2,V3,V4],xi=0.7..1.0,color=[red,green,blue,black],title="w - modes Tolamn VII");

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

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

> vsj:=subs(R=1,gamma=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 Tolman VII");

>