View source for Arnowitt-Deser-Misner energy

==Introduction==
Because of the [[equivalence principle]], there is no generally meaningful local [[energy-density]] or [[stress tensor-density]] for the [[gravitational field]]. This absence was the obstacle to development of the correct global conserved quantities, namely four-momentum and angular momentum, since the corresponding special relativistic invariances under translations and rotations are only realized asymptotically. This problem can be illuminated by an analogy to the more familiar [[gauge theories |vector gauge fields]], and the corresponding contrast there between the abelian—hence uncharged—Maxwell field and the non-abelian Yang-Mills (YM) system which is "charged", namely self-interacting. Definition of color charge in the latter theory (already classically) requires a similar (but less physical) asymptotic "color flatness"; like energy density, color charge density is gauge-dependent. Indeed, a clear picture of the Yang-Mills charge was only given (Abbott and Deser 1982b) after that for energy of cosmological gravity (Abbott and Deser 1982a), where the detailed mechanism of asymptotic [[Killing vector |Killing vectors]] was first developed. Once the latter's role was understood, it also became clear how to extend the conserved charge/energy idea to more general systems, such as higher order gravity involving higher orders of curvature (Deser and Tekin 2003, 2007), or to topologically massive models involving Chern-Simons terms (Deser et al. 1982).