Re: Time dilation in R-W Metric ?

dynamics_at_vianet.on.ca
Date: 01/08/05 

Date: Sat, 8 Jan 2005 22:07:58 +0000 (UTC)

E. Hardy wrote:
> The following question has arisen in an interdisciplinary
> application:
>
> Assuming a cosmological model with a constant mass density
> (motionless dust): Will a clock run at a different rate if the
> mass density parameter is varied?

Interesting, IMO...
Einstein's Law G_uv = T_uv looks applicable.

> I.e.: Suppose we have two identical Universes one with
> mass density A and another with mass density B.
> Will the the clocks appear to run at different rates in the
> two Universes?

Approximately,

G_00 = del^2 g_00 = T_00

(see Weinberg's "Grav & Cosmo" Eq.(7.1.7)).

The universe with the greater density T'_00
will have a more affected g'_00.

Set one universe to be a vacuum, then T_00=0
and g_00=1.

Set a universe' with density>0 to T'_00,
and g'_00 < 1.

There could always be something tricky in
such a hypothetical situation though.
Ken S. Tucker

 
> Thanks for your comments, Ernest Hardy

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