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How great is the gravitational time dilation close to a neutron star? How would the effects of gravitational time dilation compare with the event horizon of a black hole?

Qmechanic
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Ben Rutherford
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    Have you looked at the Wikipedia entry for gravitational time dilation? – Kyle Kanos Jan 29 '17 at 11:57
  • Kyle Kanos - thank you, an interesting and informative link. But as I have neither the ability to perform the calculations nor the information to put into them, it doesn't answer my question. I was hoping for a non-mathematical answer. For example, I am aware that to an outside observer things crossing the event horizon of a black hole appear to freeze because time is slowed so much. What would an outside observer see if they were watching something falling toward a neutron star in comparison to a black hole? – Ben Rutherford Jan 29 '17 at 17:12
  • ..I have neither the ability to perform the calculations nor the information... If you have a calculator, you have the ability; if you have the internet you can certainly get the information, both of which answer the question you asked. The question it seems you wanted to ask appears to be very different than what you wrote. – Kyle Kanos Jan 29 '17 at 18:25

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As it says in the Wikipedia article referred to by Kyle, the relevant formula applicable to clocks situated in the gravitational field of a spherically symmetric object is that an observer at infinity sees a clock in the gravitational field slowed by a factor $(1 - r_s/r)^{-1/2}$, where $r_s$ is the Schwarzschild radius.

For a non-rotating black hole, the Schwarzschild radius marks the event horizon and at $r = r_s = 2GM/c^2$, and the time dilation becomes infinite.

Neutron stars have radii that are at least $\sim 1.5$ times their Schwarzschild radii, and more likely closer to 2 times as big. Thus typical time dilation factors at their surfaces are 1.7 to 1.4.

A clock falling towards a neutron star will appear to run slower as it falls inwards until it reaches these maximum dilation factors just as it hits the neutron star surface. Unlike for a black hole, an external observer will see objects hitting the neutron star surface in a finite time. This phenomenon is observed in X-ray bursters.

ProfRob
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