I've been trying to work out something and I've hit a wall of stupid.(adsbygoogle = window.adsbygoogle || []).push({});

Imagine a clock a certain distance r from a large isolated spherically symmetric object of mass M. The rate at which the clock runs compared to the far away time is given by the Schwarzschild relation:

[tex]d \tau ^2 = \biggl (1- \frac{2M}{r} \biggr ) dt^2 - \frac{dr^2}{ \biggl (1- \frac{2M}{r} \biggr ) } - r^2 d \phi ^2 [/tex]

That's fine. But let's suppose that the clock has a finite mass [tex]m_c[/tex] (as clocks normally do). In that case, there will be a further time dilation due to that mass.

How do I calculate that extra dilation?

Thanks in advance.

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# Gravitational time dilation due to one's own mass

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