Do any coordinate systems include self magnification?

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Take a neutron star, its surface will be gravitationally self magnified so that it looks bigger to the distant observer, than it 'really' is, plus you can see some of the rear facing surface.

If you take the centre of the neutron star, then this process must go on there also, although unseen.

I was wondering if any coordinate system incorporated this process, say by building the shape of space from the inside of the neutron star, outwards, as the distant observer might 'see' it..?
 

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stefan r
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If you take the centre of the neutron star, then this process must go on there also, although unseen...
...
From the center of the neutron star the neutron star occupies 360 degrees same as center of Earth. From the surface of the neutron star the neutron star occupies 180 degrees same as surface of Earth. You could see stars that should be over the horizon.
 
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From the center of the neutron star the neutron star occupies 360 degrees same as center of Earth. From the surface of the neutron star the neutron star occupies 180 degrees same as surface of Earth. You could see stars that should be over the horizon.
a distant observer can see more than 50% of the neutron star's surface.

4335232013_3755299c6c_o.jpg
 

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stefan r
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a distant observer can see more than 50% of the neutron star's surface.

View attachment 228304
That picture is nice. An observer on that equator would see 180 degrees of neutron star and 180 degrees (180° by 360°) of space same as an observer on Earth.

The sky would include more than 180 degrees of the constellations. Suppose the neutron star was near Earth and spinning on Earth's axis. An observer at the surface equator would be able to see both the southern cross and Polaris. A time-lapse photo would show non-circular rings around Polaris. Orion and Taurus could be visible on one horizon while both Lyra and Bootes were still visible on the other. When a star set it would rise on the other horizon in much less than a day. Orion would be thin at rising, get fat while overhead and then tighten his belt before setting. It would still look like a 180 degree dome. If the Sun was in orbit then it would be daylight for much more than half the day even at the equator at equinox. You would get white nights at mid latitudes during the summers.
 

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