Einstein actually arrives at his stellar game changing prediction by solving the null geodesic equation (eq. 73)
gμνxμxν = 0
under the conditions of Huygens' principle expressed as
dB = (∂ϒ/∂x1)dx2
Both equations are expressed in tensors. So I don't think a special coordinate system was...
The equation is:
B = ∫(∂γ/∂x1)dx2
where B is the deflection, γ is the speed of light in units of c, and the subscript notation is used to index tensors.
This is found on page 163 in Section 22 of The Principle of Relativity, Dover Publications, 1952.
In deriving the expression for the deflection Φ of light around a massive body, invoking Huygens' principle, Einstein arrived at the equation:
dΦ/dx2 = dγ/dx1
where γ is the speed of light in units of c, and the xμ are space coordinates.
How is this equation arrived at?
Please consider the following:
Assuming a simple harmonic oscillation of the gravitational potential centered at -GM/l, and with extrema labeled 1 and 2, then:
a. the shifts in the potential are equal and opposite:
-(GM/l - GM/r1) = -(-(GM/l - GM/r2))
Dividing by GM reveals l as the...