- ADM energy
In

theoretical physics , the**ADM energy**(short for Richard**A**rnowitt, Stanley**D**eser and Charles**M**isner) is a special way to define theenergy ingeneral relativity which is only applicable to some special geometries ofspacetime that asymptotically approach a well-definedmetric tensor at infinity — for example a spacetime that asymptotically approachesMinkowski space . The ADM energy in these cases is defined as a function of the deviation of the metric tensor from its prescribed asymptotic form. In other words, the ADM energy is computed as the strength of the gravitational field at infinity.The quantity is also called the

**ADM Hamiltonian**, especially if one finds a different formula than the definition above that however leads to the same result.If the required asymptotic form is time-independent (such as the Minkowski space itself), then it respects the time-translational

symmetry .Noether's theorem then implies that the ADM energy is conserved. According to general relativity, the conservation law for the total energy does not hold in more general, time-dependent backgrounds - for example, it is completely violated inphysical cosmology .Cosmic inflation in particular is able to produce energy (and mass) from "nothing" because thevacuum energy density is roughly constant, but the volume of the Universe grows exponentially.**ee also***

ADM formalism

*Mass in general relativity **References*** R. Arnowitt, S. Deser, C. Misner: "Coordinate Invariance and Energy Expressions in General Relativity", Phys. Rev.

**122**(1961) 997-1006.

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