Book on optics in curved space-time

Question

As evidenced from my earlier questions on vision and curved space, I am struggling a little bit with visual perception in curved space-time.

I would like a book recommendation on optics and vision in curved space-time.

1. I find books on Gravitational lensing to be inadequate as Gravitational lensing itself deals mostly with specific cases in astronomy. It does not have the breadth and scope I require.

2. I want the book to discuss in detail how space (of low curvature) could affect visual perception in everyday life scenarios. Very high mathematical rigor is desired.

3. I would also really like the book to have pretty colors and pictures for aesthetic value.

If you know any book that come close to satisfying my conditions, please do tell me. I will be very grateful if you can.

Also, as per the books policy, it is also OK to provide an explanation for any subdiscipline of this topic instead, especially if that subdiscipline is not covered by most resources. But please do not make such an answer Community Wiki.

This post imported from StackExchange Physics at 2014-03-05 14:45 (UCT), posted by SE-user dj_mummy

Answer 1

Just came across your question, have you found an answer?

I don't know of any specific books but since you mentioned a desire for "very high mathematical rigor," why not just impose some arbitrary metric yourself, from a curved manifold, then solve for the geodesics? The results could be quite interesting depending on what metric is chosen.

You will of course solve the equation for null geodesics:

$${{{d^{\,2}}{q^j}} \over {d{s^2}}} + \Gamma _{k\,l}^j{{{d^{\,2}}{q^k}} \over {d{s^2}}}{{{d^{\,2}}{q^l}} \over {d{s^2}}} = 0$$

where the connection coefficients are calculated from the metric. Any number of generalizations or specializations could be imposed, e.g., Riemannian manifold, non-symmetric connection, etc.

Indeed, you could even cast Fermat's principle in this form.

Note: I added this in the spirit of your post which states that: "... it is also OK to provide an explanation for any sub discipline ..."

This post imported from StackExchange Physics at 2014-03-05 14:45 (UCT), posted by SE-user roybatty