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I enjoy thinking about theoretical astrophysics because I want to understand black holes. Given that no one understands black holes, I like to ponder the nearest thing to a black hole: a neutron star! I have searched around the web for pedagogical discussions of the structure of neutron stars such as this link from NASA: http://heasarc.nasa.gov/docs/objects/binaries/neutron_star_structure.html, but none seems to be at an advanced enough level for my liking. The problem is that I do not know what literature I should read in order to learn more.

What is the current state of neutron star research? What are some good review articles?

More specifically, I am curious about theoretical predictions for "starquakes" referenced in the link above, and how they would look to an observer on Earth. I would also be interested in understanding what happens to gas falling into a neutron star -- specifically, if Sol was spiralling to its death by neutron star.

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Kernel, I added the astrophysics. Moreover, I rephrased the title (I hope you like it, if not - let me know). –  Piotr Migdal Feb 2 '12 at 19:45
    
Looks good! Thanks, Piotr. –  Kernel Feb 5 '12 at 4:21
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I'd warn you that neutron stars are in fact (at least classically) much more complicated objects than black holes. –  Jerry Schirmer Feb 10 '12 at 13:50
    
I'm OK with that :D –  Kernel Feb 11 '12 at 21:37
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up vote 6 down vote accepted

There are a few standard textbooks on neutron star.

For interior structure and nuclear physics side two books by Glendenning are good.

http://www-nsdth.lbl.gov/~nkg/description.html

For more general relativity side Shapiro and Teukolsky has been a standard texk book for many years.

http://www.amazon.com/Black-Holes-White-Dwarfs-Neutron/dp/0471873160

Finally, if you seek for real rigor, a new book by Friedman & Stergioulas is must.

http://www.amazon.com/Rotating-Relativistic-Stergioulas-Cambridge-Monographs/dp/0521872545

There are several review papers including two in Living Review.

http://relativity.livingreviews.org/Articles/lrr-2003-3/

http://relativity.livingreviews.org/Articles/lrr-2007-1/

Several by Lattimer and Prakash are also good starting point. For example,

http://arxiv.org/abs/astro-ph/0612440

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