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)
Gamma.nonzero()
Ric.nonzero()
#Rie.nonzero()
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 :
pprint_Gamma_udd(i,k,l)
print'-'*40
print'Ricci tensor:'
for i in [0,1,2,3]:
for j in [0,1,2,3]:
if Ric.dd(i,j) !=0:
pprint_Ric_dd(i,j)
print '-'*40
#Solving EFE for A and B
s = ( Ric.dd(1,1)/ A(r) ) + ( Ric.dd(0,0)/ B(r) )
pprint (s)
t = dsolve(s, A(r))
pprint(t)
metric = gdd.subs(A(r), t)
print "metric:"
pprint(metric)
r22 = Ric.dd(3,3).subs( A(r), 1/B(r))
h = dsolve( r22, B(r) )
pprint(h)
Rs =Rscalar(Ric)
print Rs.value()
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) )
pprint (s)
t = dsolve(s, A(r))
pprint(t)
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)
G = ET(Ric, g, Rs)
print 'Initial metric:'
pprint(g.matrix())
C.nonzero()
Ric.nonzero()
#Rie.nonzero()
#Rs.printing()
G.nonzero()
print '-' * 40
#Solving EFE for A and B
s = (Ric.dd(1, 1) / A(r)) + (Ric.dd(0, 0) / B(r))
#pprint (s)
t = dsolve(s, A(r))
