MathGroup Archive 2013

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: computation of two-point objects

  • To: mathgroup at
  • Subject: [mg131226] Re: computation of two-point objects
  • From: Roland Franzius <roland.franzius at>
  • Date: Wed, 19 Jun 2013 01:26:49 -0400 (EDT)
  • Delivered-to:
  • Delivered-to:
  • Delivered-to:
  • Delivered-to:
  • References: <kph81g$2fc$>

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

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

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

  • Prev by Date: Re: Calculation of a not so simple integral
  • Next by Date: Re: How does one get data out of a TemporalData object?
  • Previous by thread: Re: computation of two-point objects
  • Next by thread: ListPlot3D