durgv.mws

> restart:

Standard Worksheet SSSPF

Durg V

Physical quatities are defined in the initialization file

> grts();

`GRTensorII Version 1.79 (R4)`

`6 February 2001`

`Developed by Peter Musgrave, Denis Pollney and Kay...

`Copyright 1994-2001 by the authors.`

`Latest version available from: http://grtensor.phy... 

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

`D:/Xitami/webpages/GRTensorJ/Metricss`

> qload(durgfive);

`Default spacetime` = durgfive

`For the durgfive spacetime:`

Coordinates

x(up)

`x `^`1` = xi, `x `^`2` = theta, `x `^`3` = phi, `x...

`Line element`

` ds`^2 = -112*R^2*(1+C*xi^2)^3*(1+6*C*xi^2)^(1/3)/...
` ds`^2 = -112*R^2*(1+C*xi^2)^3*(1+6*C*xi^2)^(1/3)/...

Constraints = [C = 1/(-11+5*alpha), K = -125/112*5^...

`M. Durgapal, J. Phys. A, 15, 2637 (1982), M. Kork...

Physical parameters

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

`CPU Time ` = .130

> 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

`CPU Time ` = .30e-1

> grdisplay(_);

`For the durgfive spacetime:`

Iso

Iso = `All components are zero`

rho

rho = 1/896*C*(120*(1+6*C*xi^2)^(4/3)*C^3*xi^6+450*...
rho = 1/896*C*(120*(1+6*C*xi^2)^(4/3)*C^3*xi^6+450*...

p

p = -1/896*C*(200*(1+6*C*xi^2)^(4/3)*C^3*xi^6+1050*...
p = -1/896*C*(200*(1+6*C*xi^2)^(4/3)*C^3*xi^6+1050*...

mass

mass = 1/224*(xi^2*R^2)^(3/2)/R^2*C*(645*(1+6*C*xi^...

Juncion conditions

> C1:=1/((-11+5*alpha));

C1 := 1/(-11+5*alpha)

> K1:=-125/112*5^(1/3)*((-1+alpha)*(-11+5*alpha)^2)^(1/3)*(-1792+2097*alpha-792*alpha^2+95*alpha^3)/(-11+5*alpha)^3/alpha;

K1 := -125/112*5^(1/3)*((-1+alpha)*(-11+5*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 Durg V");

[Maple Plot]

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 Durg V");

[Maple Plot]

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 Durg V");

[Maple Plot]

Trapping

Potential impac parameter

> B:=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=3.00,Bj):

> B2:=subs(alpha=2.9,Bj):

> B3:=subs(alpha=2.8,Bj):

> B4:=subs(alpha=2.7,Bj):

> plot([B1,B2,B3,B4],xi=0.0..1,color=[red,green,blue,black],title="Trapping Durg V");

[Maple Plot]

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=3.0,Vj):

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

> V3:=subs(alpha=2.8,Vj):

> V4:=subs(alpha=2.7,Vj):

> plot([V1,V2,V3,V4],xi=0.3..1.0,color=[red,green,blue,black],title="w - modes Durg V");

[Maple Plot]

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

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

> vsj:=subs(R=1,C=C1,K=K1,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=3.5,vsj):

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

[Maple Plot]

>