Well via Special Relativity anything moving relative to the Earth will appear to have a slowed time frame. We could exchange messages via light with clock timestamps and we would see that their clocks run slower than ours, but then they would also conclude our clocks are running slower than their's. No paradox that's just the nature of space-time.

Sounds although General Relativity is more what you're interested is as time also depends on the strength fo the gravitational field you are in. So clocks on the surface of the Sun run slower than on the Earth, and now the exchange of message would conclude clock on the Sun really are running slower. 

So the slowest clocks would be on the surface of a neutron star (theoretically floating above the event horizon of a black hole would be the ultimately slow clock, but it's not a very tenable position for a clock to hold)

Robert,

"So the slowest clocks would be on the surface of a neutron star.."

In the core of the neutron star..

Yes indeed you have a point, you can get some extra deeper potential going to the core (but also not very tenable place for a clock).

I must admit I was think in terms of clocks you could in principle observe (like emission lines).

Robert,

It is not even small the extra negative potential... considering  the excursion of the potential between the surface and the center, it is about the same as the surface and the deep space in case of Earth at least... I agree, it is impossible to measure for the core of a neutron star ..

Hi Stef,

   Agreed, which leads to one question I've always had "Where does the event horizon form when a neutron star collapses?" I've pictured it being in the core when enough mass collects and then sweeping outwards, which is probably too simple.

Hi Robert,

Difficult to conceive it differently...it should start from a Planck lenght right in the center then extend progressively... where GR ceases to be valid (provided that it is actually valid elsewhere)...