Gravitational Chern-Simons terms and black hole entropy. Global aspects

Understand

We discuss the topological and global gauge properties of the formula for a black hole entropy due to a purely gravitational Chern-Simons term.

• We study under what topological and geometrical conditions this formula is well-defined.
• To this end we have to analyze the global properties of the Chern-Simons term itself and the quantization of its coupling.
• We show that in some cases the coupling quantization may interfere with the well-definiteness of the entropy formula.