Re: computation of two-point objects
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- Subject: [mg131226] Re: computation of two-point objects
- From: Roland Franzius <roland.franzius at uos.de>
- Date: Wed, 19 Jun 2013 01:26:49 -0400 (EDT)
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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(r-2\sigma v)(d\theta^2+\sin(\theta)^2d\phi^2)
> \phi=\n(1-2\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[(1-2\sigma v/r)/2, v] dv + D[(1-2\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 Euler-Lagrange equations for geodesics
D[pv/.momenta, t] -D[L,dv[t]] == 0
and calulate Riemann and Ricci.
--
Roland Franzius