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() Rs.printing() print '-' * 40 #Solving EFE for A and B
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() Rs.printing() print '-'*40
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) t = dsolve(s, A(r)) pprint(t) metric = g.matrix().subs(A(r), t) print "metric:" pprint(metric) r22 = Ric.dd(3,3).subs( A(r), 1/B(r))
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) t = dsolve(s, A(r)) pprint(t) metric = g.matrix().subs(A(r), t) print "metric:" pprint(metric) r22 = Ric.dd(3, 3).subs(A(r), 1 / B(r))