Re: computation of two-point objects

*To*: mathgroup at smc.vnet.net*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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <kph81g$2fc$1@smc.vnet.net>

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