Deflection of light around a neutron star

[quasar_4]

Homework Statement

If a neutron star were bright enough to see its surface with a telescope, we'd be able to see not just the hemisphere facing toward us but also part of the far hemisphere. Explain why and estimate the latitude above which the far side could be seen.

Homework Equations

Deflection of light due to gravity
Schwarzschild metric

The Attempt at a Solution

I think I have some understanding of why this occurs - it's just a result of the deflection of light around the neutron star (reflected light on the far hemisphere is deflected around the side of the neutron star, if I'm thinking about this correctly). But what I'm having trouble with is the estimate. In the Schwarzschild geometry, we're dealing with a static, spherical star -- so why the minimum latitude? Shouldn't the light be deflected evenly around the neutron star, regardless of latitude?

And how could I come up with an estimate? I'm a bit perplexed.

 

[diazona]

I think the problem may be talking about looking "down" at a neutron star from its north pole. So when it asks about latitude, it's just asking you how far into the far hemisphere you'd be able to see (in terms of an angle).

As for actually doing the problem, I'd think about null geodesics in the Schwarzschild metric. Specifically, think about a light ray that you, a distant observer, would perceive as being at the very edge of the star's image, and imagine "tracing" it back to its source. That might give you some idea about where to start with the math.

Then again, it only says to come up with an estimate, not necessarily an actual solution, so maybe you could find some sort of calculation that would be almost equivalent but much easier? Maybe like the deflection of light around the Sun (only with a neutron star instead of the Sun).