from Ricci import *
from Rscalar import *
from ET import *
B = Function('B')
A = Function('A')
t = Symbol('t')
r = Symbol('r')
theta = Symbol('theta')
phi = Symbol('phi')
g = Metric((-B(r), 0, 0, 0), (0, A(r), 0, 0), (0, 0, r**2, 0),
(0, 0, 0, r**2 * sin(theta)**2))
x = (t, r, theta, phi)
C = Christoffel(g, x)
Rie = Riemann(C, x)
Ric = Ricci(Rie, x)
Rs = Rscalar(Ric)
G = ET(Ric, g, Rs)
print 'Initial metric:'
pprint(g.matrix())
#C.nonzero()
Ric.nonzero()
#Rie.nonzero()
#Rs.printing()
G.nonzero()
print 'Initial metric:'
pprint(gdd)
t=Symbol('t')
r=Symbol('r')
theta=Symbol('theta')
phi=Symbol('phi')
A= Function('A')
K = Symbol('K')
#general, spherically symmetric metric
gdd=Matrix((
(-1,0,0,0),
(0, A(t)/(1 - K*r**2), 0, 0),
(0, 0, A(t)*r**2, 0),
(0, 0, 0, A(t)*r**2*sin(theta)**2)
))
g=Metric(gdd)
x=(t,r,theta,phi)
C=Christoffel(g,x)
Rie = Riemann(C,x)
Ric=Ricci( Rie,x)
Rs =Rscalar(Ric)
print 'Initial metric:'
pprint(gdd)
C.nonzero()
Ric.nonzero()
#Rie.nonzero()
#Rs.printing()
t=Symbol('t')
r=Symbol('r')
theta=Symbol('theta')
phi=Symbol('phi')
#general, spherically symmetric metric
gdd=Matrix((
(-B(r),0,0,0),
(0, A(r), 0, 0),
(0, 0, r**2, 0),
(0, 0, 0, r**2*sin(theta)**2)
))
g=Metric(gdd)
X=(t,r,theta,phi)
Gamma=Christoffel(g,X)
Rie = Riemann(Gamma,X)
Ric=Ricci(Rie,X)
Rs =Rscalar(Ric)
print 'Initial metric:'
pprint(gdd)
Gamma.nonzero()
Ric.nonzero()
#Rie.nonzero()
Rs.printing()
print '-'*40
#Solving EFE for A and B
s = ( Ric.dd(1,1)/ A(r) ) + ( Ric.dd(0,0)/ B(r) )
t=Symbol('t')
r=Symbol('r')
theta=Symbol('theta')
phi=Symbol('phi')
#general, spherically symmetric metric
gdd=Matrix((
(-B(r),0,0,0),
(0, A(r), 0, 0),
(0, 0, r**2, 0),
(0, 0, 0, r**2*sin(theta)**2)
))
g=Metric(gdd)
X=(t,r,theta,phi)
Gamma=Christoffel(g,X)
Ric=Ricci(Riemann(Gamma,X),X)
def pprint_Gamma_udd(i,k,l):
pprint(Eq(Symbol('Gamma^%i_%i%i' % (i,k,l)), Gamma.udd(i,k,l)))
def pprint_Ric_dd(i,j):
pprint(Eq(Symbol('R_%i%i' % (i,j)), Ric.dd(i,j)))
print 'Initial metric:'
pprint(gdd)
print '-'*40
print 'Christoffel symbols:'
for i in [0,1,2,3]:
for k in [0,1,2,3]:
for l in [0,1,2,3]:
from Rscalar import *
B = Function('B')
A = Function('A')
t = Symbol('t')
r = Symbol('r')
theta = Symbol('theta')
phi = Symbol('phi')
#general, spherically symmetric metric
g = Metric(((-B(r), 0, 0, 0), (0, A(r), 0, 0), (0, 0, r**2, 0),
(0, 0, 0, r**2 * sin(theta)**2)))
x = (t, r, theta, phi)
C = Christoffel(g, x)
Rie = Riemann(C, x)
Ric = Ricci(Rie, x)
Rs = Rscalar(Ric)
print 'Initial metric:'
pprint(g.matrix())
C.nonzero()
Ric.nonzero()
#Rie.nonzero()
Rs.printing()
print '-' * 40
#Solving EFE for A and B
s = (Ric.dd(1, 1) / A(r)) + (Ric.dd(0, 0) / B(r))
#pprint (s)
from sympy import *
from Riemann import *
R = Symbol('R')
theta = Symbol('theta')
phi = Symbol('phi')
g = Metric((theta, phi))
g[-0, -0] = 1
g[-1, -1] = R**2 * (sin(theta))**2
print(g.components.keys())
g.invert()
C = Christoffel(g)
R = Riemann(C)
Ric = Ricci(R)
Rs = RicciScalar(g, Ric)
print "Christoffel: "
for i in range(len(C.nonzero)):
print(str(C.nonzero[i][0]) + ":")
print(cancel(C.nonzero[i][1]))
print "The components of the Ricci tensor for a FLRW universe are: "
for i in range(len(Ric.nonzero)):
print(str(Ric.nonzero[i][0]) + ":")
print(cancel(Ric.nonzero[i][1]))
for i in range(len(C.nonzero)):
print(str(C.nonzero[i][0]) + ":")
print(C.nonzero[i][1])
G = EnMt(g, Ric, Rs)
t=Symbol('t')
r=Symbol('r')
theta=Symbol('theta')
phi=Symbol('phi')
#general, spherically symmetric metric
gdd=Matrix((
(-B(r),0,0,0),
(0, A(r), 0, 0),
(0, 0, r**2, 0),
(0, 0, 0, r**2*sin(theta)**2)
))
g=Metric(gdd)
X=(t,r,theta,phi)
Gamma=Christoffel(g,X)
Rie = Riemann(Gamma,X)
Ric=Ricci(Rie,X)
print 'Initial metric:'
pprint(gdd)
print '-'*40
print 'Christoffel symbols:'
for i in [0,1,2,3]:
for k in [0,1,2,3]:
for l in [0,1,2,3]:
if Gamma.udd(i,k,l) != 0 :
Gamma.printing(i,k,l)
print'-'*40
print'Ricci tensor:'