General Relativity/Stoke's theorem

Stokes' Theorem states that if there is an n-dimensional orientable manifold ${\displaystyle {\mathcal {M}}}$ with boundary ${\displaystyle \partial {\mathcal {M}}}$, and if there is a form ${\displaystyle \omega }$ (with compact support) defined on the manifold, then the following is true:

${\displaystyle \int _{\mathcal {M}}d\omega =\int _{\partial {\mathcal {M}}}\omega }$