PSR J1748-2446ad is the fastest spinning pulsar with a rotation of over 700 times per second. It has the mass of two suns and a diameter of just over 30km. This means that a person on the equator would be traveling at .25c. If I were to land on the surface, what would I experience between the crushing gravity and the centrifical (I know tht doesn’t really exist) force. At those relativistic speeds, what distortion would I observe looking up in the sky?
First off, as you approach it the intense magnetic field will wipe your brain, and then tear the tissues of your body apart due to the dimagnetism of water. The escape velocity for a neuton star is about 1/3 c, so you’d be accelerated to that speed by it’s gravity before you went splat on the surface.
If you could magically protect yourself on the surface, I’m not quite sure what spinning at 0.25c would do to your view. Time dilation might not be particularly significant at that speed, but blue and red shifting of light would be, looking around there would be a gradient effect. North and south the surface would appear with it’s true colour, but looking east or west one view would be significantly bluer and brighter than the other, depending on which way the star is rotating. Also, due to the enormous gravitational field, you’d be able to look some way beyond the normal horizon, due to light travelling in a curved path.
Looking up, everything would be a blur, as you are rotating at 700 times a second. Expect to feel dizzy. The gradient and bending of light would also affect the appearance of objects in the sky. If you could pick out a star as it rose on the horizon, it would initially appear bluer than normal. It would rise quickly at first before slowing as it reached it’s zenith, as light is bent more the closer the object is to the neutron star’s horizon. (Actually, this may not be noticeable, as you are in effect looking beyond the horizon when the star first comes into view). As it rose and then set it would become redder and dimmer.
I’d welcome any corrections to the above. I don’t know what the intense magnetic field would do to your view, according to wikipedia “In a field of about 10[sup]5[/sup] teslas atomic orbitals deform into rod shapes.”. The magnetic field at the surface of a normal neutrol star is about three orders of magnitude higher.
It’s “centrifugal” (“center-fleeing”). And it’s a perfectly respectable concept in a rotating (thus, non-inertial) frame of reference.
This made me smile to myself. 
I’m not sure you would. The reference frame of the sky wouldn’t be a blur - it’d just be lines, as it is essentially a television screen with a 700 fps refresh rate. Would your brain be even able to process those speeds? Would your inner ear register that as “moving” at all?
Yes, starfields would appear as series of lines, that’s a better way of putting it. The lines would be bluer and brighter at the rising horizon than the setting horizon. If you could focus on a single star, which would require super-human reflexes, it would appear as I described above.
I’m sure there would be far too much glare from the surface to see anything in the sky, but the atmosphere is only about a metre thick, and anyone who isn’t a midget will have their heads above it. With no atmosphere to scatter surface light, it might be possible to see object in the sky by wearing blinkers.
“Dizzy” was tongue in cheek, it really would be the least of your problems in such an extreme environment. If my calculation is correct, the star’s rotation would exert a centrifugal force of about six and a half million g on someone standing on the surface. That sounds a lot, but is trivial compared to the surface gravity of about 10[sup]11[/sup] g. You’d be subject to a huge tidal force, due to the difference in gravity at ground and head level. Carelessly drop a handful of change and it will hit the surface at about 7 million kph and explode. To stand on a neutron star you need to be of at least demi-god status.
Don’t forget that you’d also have gravitational blueshifts to deal with, when looking at the stars.
Good point, everything in the sky is going to be blue-shifted. Objects rising in the sky are going to be blue-shifted the most, while those setting will be blue-shifted the least.