- #1

- 1,728

- 13

## Homework Statement

(a) Find the proper time in the rest frame of particle

(b) Find the proper time in the laboratory frame

(c) Find the proper time in a photon that travels from A to B in time P

## Homework Equations

## The Attempt at a Solution

__Part(a)__

[/B]

The metric is given by:

[tex] ds^2 = -\left( 1 - \frac{2GM}{c^2r} \right) c^2 dt^2 + \left( 1 + \frac{2GM}{c^2r} \right) dr^2 [/tex]

Circular orbit implies that ##dr^2 = 0##, so

[tex]ds^2 = c^2 d\tau^2 = -\left( 1 - \frac{2GM}{c^2R} \right) c^2 dt^2 [/tex]

[tex] \left( \frac{d\tau}{dt} \right)^2 = \left( 1 - \frac{2GM}{c^2R} \right) [/tex]

[tex] \frac{d\tau}{dt} = \sqrt { \left( 1 - \frac{2GM}{c^2R} \right) } [/tex]

Since the time between event A and B is ##dt = P##, the time experienced in the rest frame must be ## d\tau = \sqrt { \left( 1 - \frac{2GM}{c^2R} \right) } P ##?

I'm not sure how to approach parts (b) and (c)..