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My question is inspired by the following answer by voix to another problem:

"There is a real object with relativistic speed of surface - millisecond pulsar. The swiftest spinning pulsar currently known, spinning 716 times a second. Surface speed of such pulsar with radius $16 \mathrm{km}$ is about $7\times10^{7} \mathrm{m/s}$ or $24\%$ speed of light."

This period of the pulsar is that measured here on Earth, that is by remote observer. However, pulsar has both enormous surface rotational speed and quite strong gravitational field. All processes at relativistic speed or strong gravity are time dilated. Is the period affected as well? What is difference of periods of rotation measured by a distant observer and an observer on the pulsar surface?

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Leos Ondra
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There is a relativistic effect, but it's very tiny at that speed (0.24c). In fact, the effect is even smaller, since only the radially most distant particles from the rotation center are traveling with 0.24c. (The speed decreases with 1/r)

See for example this nice plot of relative mass vs. velocity, taken from gutenberg.org

P.S.: I calculated the mass change of a pulsar due to relativistic rotation a long long time ago ;-) (integrated over the whole sphere–no voodoo–taking the correct angular velocity into account) and as far as I can remember, the effect was far below 1%.

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tamasgal
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  • I would guess that solely the gravitational dilation would slow the time by about 15 percent... – Leos Ondra May 10 '13 at 18:02
  • But that doesn't mean, that the pulsar is rotating 0.15 slower in the observers space-time. Also the time dilation of a particle in the pulsars system changes periodically, since it's relative speed is not constant compared to the observer (going back and forth). That's basically the same effect when you observe a rotating galaxy and see a red shift on the one side and a blue one on the opposite side. – tamasgal May 10 '13 at 18:07
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    "But that doesn't mean, that the pulsar is rotating 0.15 slower in the observers space-time". Why? – Leos Ondra May 18 '13 at 10:12