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If one were to consider a classical particle in a box of length L in Minkowski space then clearly the time taken to go between the walls of the box is L/v with v velocity.

In the GR case with some metric coefficients A(r) and B(r) (spherically symmetric system, say) it's clear that the distance traveled is longer and so the period should be longer as well, my question is how to calculate this? Let's say m = 0 so v = c.

Do I take dt = 0 and integrate the line element ds from 0 to L over dr? I thought of trying to take the already computed flat space period and applying the time dilation method to it but that contains a radial coordinate component (obviously as it must be position dependent) but i'm unsure as to how to 'get rid' of this part, i.e. would r here simply represent the end points or again is some integral/averaging needed?

I know this is probably kind of a trivial question but still it's doing my head in a bit =P

Cheers

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# Gravitational effects on particles orbit in a box

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