> restart:

Standard Worksheet SSSPF

Nariai IV

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(niva);

Physical parameters

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

Junction conditions

> f1:=subs(beta=1/alpha,sqrt(3)*sqrt((2+beta+2*sqrt(1-2*beta))/(12+beta))):

> k1:=-1/2*sqrt(3)*sqrt(1/alpha):

> c1:=1/(sqrt(1+(1-f1^2)*(7*f1^2-3)^2/(2*f1^2*(5*f1^2-3)^2))):

Perssure plots

> pj:=subs(c=c1,k=k1,f=f1,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 Nariai IV");

Energy density plots

> rhoj:=subs(c=c1,k=k1,f=f1,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 Nariai IV");

Mass plots

> mj:=subs(c=c1,k=k1,f=f1,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 Nariai IV");

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,f=f1,B):

> B1:=subs(alpha=3.1,Bj):

> B2:=subs(alpha=3.11,Bj):

> B3:=subs(alpha=3.12,Bj):

> B4:=subs(alpha=3.13,Bj):

> plot([B1,B2,B3,B4],xi=0.75..0.95,color=[red,green,blue,black],title="Trapping Nariai IV");

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,f=f1,V):

> V1:=subs(alpha=2.96,Vj):

> V2:=subs(alpha=2.97,Vj):

> V3:=subs(alpha=3,Vj):

> V4:=subs(alpha=3.04,Vj):

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

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,vsj):

> plot([vs1,vs2,vs3,vs4],xi=0..1,color=[red,green,blue,black],title="V Nariai IV");

>