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Re: computation of twopoint objects
Posted:
Jun 19, 2013 1:21 AM


Am 15.06.2013 10:18, schrieb Mark Roberts: > hello, > I have been stuck for decades trying to calculate the world function for > > ds^2=(1+2\sigma)dv^2+2dvdr+r(r2\sigma v)(d\theta^2+\sin(\theta)^2d\phi^2) > \phi=\n(12\sigma v/r)/2 > R_{ab}=2\phi_a\phi_b > > one gets elliptic functions if one try direct method, The trouble with > approximations is that it is hard to tell if they converge..... > > bye,
Did you try Zimmerman/Olness chapter 10 methods in
http://library.wolfram.com/infocenter/Books/4539
The other simple way is to use the geometrical Lagrangian method
Define the Lagrangian
Lagrangian =1/2 ds2 /. dphi> D[(12\sigma v/r)/2, v] dv + D[(12\sigma v/r)/2, r] dr
and momenta = {Pv > D[Lagrangian,dv], Pr> D[Lagrangian,dr], Ptheta > D[L,dtheta} }
Then prepare all variables with a time argument [t] and read the table of Christoffel symbols off from the EulerLagrange equations for geodesics
D[pv/.momenta, t] D[L,dv[t]] == 0
and calulate Riemann and Ricci.

Roland Franzius



