Solution strategy for linearized gravity problem

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The discussion revolves around solving a linearized gravity problem involving a mass moving in the x-direction and the trajectory of a photon falling freely in the y-direction. Participants emphasize the importance of transforming to the rest frame of the moving mass to simplify the problem, while clarifying that linearized gravity does not imply a flat spacetime. The metric provided is not flat due to the presence of the gravitational potential term, and the Riemann tensor does not vanish, indicating curvature. The conversation also touches on the limitations of Lorentz transformations in this context and the necessity of adhering to the Lorentz gauge for proper metric transformations. Ultimately, the focus is on deriving the correct equations of motion for the photon based on the given conditions.
  • #31
Jonsson said:
That is a good thing, because we are not interested in all null paths.

Isn't a photon trajectory a null path?

Jonsson said:
Yes, I agree these solve (*), but why is it important that you've found exactly one solution that don't interest us?

Because what I found isn't a geodesic but is a solution to (*). So (*) isn't a complete specification of the geodesic problem statement.

Jonsson said:
Can you propose some strategy that will work?

yes, solve the geodesic problem for the metric you've been given then transform the answer to the ##M## is in motion frame?
 
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  • #32
Paul Colby said:
yes, solve the geodesic problem for the metric you've been given then transform the answer to the ##M## is in motion frame?

Thanks. I found the deflection angle is ##\frac{4GM}{b}##. How do you say I transform this quantity back?
 

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