I am currently doing an undergraduate project about Gauss-Bonnet-Chern Theorem. Is there any particular books/papers regarding the application of the theorem in the theory of general relativity?

## 1 Answer

Gauss-Bonnet is used extensively in the proofs of “no-hair” and “positive mass”:

*Israel, Werner*, **Event Horizons in Static Vacuum Space-Times**, Phys. Rev. 164, 1776-1779 (1967).

*Schoen, Richard; Yau, Shing-Tung*, **On the proof of the positive mass conjecture in general relativity**, Commun. Math. Phys. 65, 45-76 (1979). ZBL0405.53045.