The ADM parametrization and applications
Horatiu Nastase · Cambridge University Press eBooks · 2025
We define the ADM parametrization of gravitational actions. Then, we define extrinsic curvature for both a spacelike hypersurface in the ADM parametrization and for a general surface embedded in a larger space. The Gauss–Codazzi equations for the embedding of a surface are defined and explained, as well as the Israel junction conditions. After defining the notion of Killing vectors, we consider asymptotically flat spacetimes, with the possible definitions of mass (Kumar, ADM, linearized) and the BMS group of asymptotic symmetries. Finally, we calculate and define the boundary term of the gravitational action, the Gibbons–Hawking–York term.