Suppose we approach a neutron star or a stellar black hole close enough, is the gravitational lens around it 3-dimensional (like a tunnel) or is it 2-dimensional? It's 3-dimensional as if you entered a spacetime tunnel, isn't it? If you entered the tunnel, sidewards you'd see the firmament distorted too, right?

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    $\begingroup$ You'll get distortions in the shape of the field if the body is not spherical, or has asymmetric internal density variations. $\endgroup$ Dec 2 '20 at 18:20
  • $\begingroup$ @WayfaringStranger What do you mean by 'not spherical'? White dwarves, neutron stars and quark stars are spherical. Do you mean black holes / singularities? $\endgroup$
    – Greenhorn
    Dec 3 '20 at 6:49
  • $\begingroup$ I'm thinking asteroids, moons, planets and the like. Doesn't really fit into your stellar question, but does put limits on when you can expect a spherical field. Come to think of it, rotating neutron stars do frame dragging, which would affect the symmetry of the gravitational field: duckduckgo.com/… $\endgroup$ Dec 3 '20 at 17:15

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