Applications of Operator Algebras to modern physics

The only applications to general relativity that I know of (my field!) is via Connes' noncommutative geometry, which is...complicated. Connes' work is freely (and legally!) available online. See also the math overflow thread Applications of Noncommutative Geometry, which may be interesting.

Operator algebras pop-up in Algebraic Quantum Field Theory too, which may be fun to look at. Actually, trying to discuss quantum fields on curved spacetime requires operator algebras.

The Physics.SX thread "Why are von Neumann Algebras important in quantum physics?" is also relevant.

You might look at Bratteli and Robinson, "Operator Algebras and Quantum Statistical Mechanics 2: Equilibrium States. Models in Quantum Statistical Mechanics http://books.google.ca/books?id=01xlGB8qVNYC