# Is radiation from neutron stars delayed by time dilation?

I understand a neutron star to be the densest stuff that can exist without becoming a black hole, the densest thing which directly gives off radiation we can detect. At the event horizon of a black hole, time stands still, in our frame of reference.

Does there exist neutron stars which are very close to getting an event horizon?

Does this "neutron star horizon" cause time dilation, a zone from within of which movement is very slow in our frame of reference?

Could it for example be that the first light from a neutron star itself reaches us billions of years after the light of the supernova of the "classical" star which created the neutron star and its event-horizon like relativistic effects?

• Well, maybe not the densest thing... en.wikipedia.org/wiki/Quark_star#Strange_stars but not really relevant here :) Good question, I think you mean dilation? – Tim May 20 '15 at 6:59
• Corrected the spelling. I still refrain from using the "proper form" which is dilatation because I don't want to sound like a shoemaker (i.e. a "snob") in a topic I don't know much about. Strange stars might exist within neutron stars. – LocalFluff May 20 '15 at 7:10

A typical neutron star of $1.5M_{\odot}$ is thought to have a radius of around 8-10 km. This is only a factor of 2 larger than the Schwarzschild radius for a similar mass black hole.

We know that more massive neutron stars do exist. The current record holder is around $2M_{\odot}$. Most equations of state (the adopted relationship between pressure and density) for dense nuclear matter suggest that more massive neutron stars are smaller and therefore must be even closer in radius to the Schwarzschild radius.

So the premise of you question is basically correct. It is certainly true that when you deal with neutron star spectra you do have to apply significant general relativistic corrections to measured temperatures and the same corrections would need to be applied to any temporal variations.

Thus a time-variable signal from a neutron star surface will appear slower to an observer on Earth.

For the last part, I suspect that the scenario you propose is extremely unlikely. Rhoades & Ruffini (1974) first established that there must be a maximum mass for a neutron star under GR conditions, even if we allow the equation of state to harden to the point where the speed of sound is the speed of light. This maximum mass is around $3.2M_{\odot}$. This sets an upper limit to the possible value of $GM/Rc^{2} \leq 0.405$ (see p.261 of Shapiro & Teukolsky, Black holes, white dwarfs and neutron stars). This in turn sets an upper limit the possible gravitational redshift (and time dilation factor) of 2.29.

Beyond this point the neutron star is unstable and will collapse to become a black hole. In reality the limit is probably a bit tighter than that because most proposed equations of state result in neutron stars becoming unstable at finite densities and at masses quite a bit lower than $3.2M_{\odot}$.

So I think the most time dilation you are ever going to see from a neutron star surface is a factor of $\sim 2$.