Exercises in expansion

I like to find simple examples which give insight into physics, and came
up with these, which I thought quite fun and that some of you might like
to try them.

Place a single stationary particle at distance r from the origin in a
flat Minkowski space-time, using spherical coordinates. Introduce primed
coordinates such that t' = t and r'= a(t)r with a^dot/a = const. Solve
the equation of motion of the particle in primed coordinates?

Now place the particle in a Schwarzschild geometry and again introduce
primed coordinates with r'= a(t)r with a^dot/a = const, and allow the
Schwarzschild geometry to contract with the primed coordinates. In other
words the geometry is Schwarzschild in primed coordinates. Show the
relationship between t and t' and solve the equations of motion in
primed and unprimed coordinates.



Regards

--
Charles Francis
substitute charles for NotI to email

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