- ADM energy
theoretical physics, the ADM energy (short for Richard Arnowitt, Stanley Deser and Charles Misner) is a special way to define the energyin general relativitywhich is only applicable to some special geometries of spacetimethat asymptotically approach a well-defined metric tensorat infinity — for example a spacetime that asymptotically approaches Minkowski 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 theoremthen 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 in physical cosmology. Cosmic inflationin particular is able to produce energy (and mass) from "nothing" because the vacuum energydensity is roughly constant, but the volume of the Universe grows exponentially.
Mass in general relativity
* R. Arnowitt, S. Deser, C. Misner: "Coordinate Invariance and Energy Expressions in General Relativity", Phys. Rev. 122 (1961) 997-1006.
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