Solution strategy for linearized gravity problem

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Homework Help Overview

The discussion revolves around a problem in linearized gravity involving a mass moving in the x direction and its effect on the trajectory of a photon. The original poster presents a metric that incorporates a gravitational potential and seeks to understand how to approach the problem of determining the new metric for the moving mass and the deflection of the photon.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of Lorentz transformations and question their applicability in the context of the given metric. There is exploration of the transformation between different coordinate systems and how to express the photon’s trajectory in these frames. Some participants express confusion about the nature of the metric and the implications of linearized gravity.

Discussion Status

The discussion is active, with participants offering various perspectives on the transformation of coordinates and the nature of the gravitational metric. There is a mix of agreement and disagreement regarding the use of Lorentz transformations, and participants are probing deeper into the implications of the problem statement and the definitions involved.

Contextual Notes

Participants note the complexity introduced by the moving mass and the need to clarify the coordinates used in the problem. There is also mention of the original poster's uncertainty about the unknown coordinates and the implications of the gravitational potential being small.

  • #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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