Re: Bending of light not well authenticated

Hi Gene et al...

Gene McGraw wrote:
> On Sat, 21 May 2005 "Koobee Wublee" wrote:
> > I get the following two equations in accordance with most
derivations
> > (r dH/dt)^2 / c^2 = (1 - 2 U)^2 b^2 / r^2
> > (dr/dt)^2 / c^2 = (1 - 2 U)^2 (1 - (1 - 2 U) b^2 / r^2)
> >Where H = angle of the photon where at perihelion H = 0
> > U = G M / c^2 / r, b = integration constant
>
> Those are indeed the equations of motion of a pulse of light (making
> allowances for your ambiguous notation of two divisions in a row).
> Hopefully you understand that those two equations are derived from
the
> metric by the variational technique (corresponding to Fermat's
> Principle of Least Time), and they represent the set of light-like
> extremal paths. So the hard work is already finished by this point,
> and all that's left is to examine the path with the appropriate
values
> of M and b to see how much deflection there is.
>
> If you really want to derive the deflection of light for general
> relativity, from scratch, you have to start with the field equations,
> derive the metric, and solve for the light-like paths to give the
> equations of motion that you cited above. From this point (which you
> seem to be taking as your starting point) it's fairly trivial to
> determine the deflection.

Ok, G_uv=0 => Schwarz... holds

> > I have (b = R) where R is the perihelion of the photon to the sun
> > with mass of the sun = 0.
>
> The mass of the sun is not zero, it is M, and the value of the
> constant of integration b is not exactly equal to M, as can be seen
> immediately from your second equation of motion above. Remember, the
> perihelion distance R is, by definition, the distance from the path
to
> the sun at the point on the path closest to the sun, and at this
> minimum point the derivative dr/dt is zero. Plug this into your
second
> equation of motion above (with r = R to signify the perihelion
> distance) and solve for b. This gives b = R / sqrt(1 - 2U). Do you
> understand this?

IMO there's a problem. You should get b=R-2*M.
That's from ds=0, C(radial)=c*g_00 = c*(1-2U).
Regards
Ken
....

.

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