- #1
DiamondGeezer
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I've been trying to work out something and I've hit a wall of stupid.
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.
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.