|   | 1 |  initial version  | 
Try this:
Man = Manifold(4, 'Man', r'\mathcal{M}')
M = var('M')
BL.<t,r,th,ph> = Man.chart(r't r:(0,+oo) th:(0,pi):\theta ph:(0,2*pi):\phi')
g = Man.lorentzian_metric('g')
function('f')(r)
g[0,0] = f(r)
g[1,1] = -1/f(r)
g[2,2] = -r^2
g[3,3] = -(r*sin(th))^2
# Christoffel symbols
nab = g.connection()
show(nab.display())
 Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.
 
                
                Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.