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If the escape velocity of a neutron star is just less than that of light, will light come out very slowly from the star?


marked as duplicate by John Rennie general-relativity Jan 10 '18 at 17:39

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    $\begingroup$ It will come out at the speed of light, but redshifted. $\endgroup$ – Ben51 Jan 10 '18 at 16:52
  • $\begingroup$ @Ben, to me, the statements strike me as equivalent. Light that is redshifted such so that it has twice the wavelength, travels half as fast in some sense - because the time between each full cycle, which is one unit of transfer, is doubled. $\endgroup$ – Steve Jan 10 '18 at 17:01
  • $\begingroup$ Ha, yes I guess one way to interpret the phrase "light comes out slowly" energy comes out more slowly than it would otherwise. $\endgroup$ – Ben51 Jan 10 '18 at 17:03
  • $\begingroup$ @Ben, it's an interesting equivalence isn't it? Because it's not just energy that has slowed down - the light wave itself has slowed down, because the same wave unit no longer fully traverses the same distance in the same period of time. $\endgroup$ – Steve Jan 10 '18 at 17:22

Particles moving at the speed of light (massless particles) and particles not moving at the speed of light (massive particles) are completely different beasts:

  • A particle moving at the speed of light will keep moving at the speed of light no matter the physical conditions or processes it went through and no matter the observer frame.
  • Particles not moving with the speed of light, on the other hand, may reach velocities close, but never equal to the speed of light in some frames. However, there will always be possible observers who would see this particle at rest.

That is, light escaping the field of any compact gravitating object, if escaping at all, will always escape at exactly the speed of light, no matter its gravitational binding. The energy required to release the photon from the gravitational potential is instead taken from its frequency (which by $E =hf$ is stores the photon energy). This is how gravitational redshift of light comes about.

When, however, we have a massive particle moving close, but not equal to the speed of light which is escaping a compact gravitating object, it will instead take the energy required to escape the potential from its speed. The speeds which are consumed by the escape of a massive particle from a neutron star are indeed quite large. Depending on the neutron-star model (we are still not sure about a lot of details about neutron stars) and depending on how generous we are with wild speculations about the neutron-star structure, the escape velocity for a massive particle might be something between $0.6-0.9$ times the speed of light.

  • $\begingroup$ Void, isn't that equivalent to what I've touched on in the comments on the question? For a massive particle, gravity robs it of its speed by slowing it's movement down. For a massless particle, gravity robs it of its speed by elongating it's wavelength, which slows its movement down. $\endgroup$ – Steve Jan 10 '18 at 17:26

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