# Derivation of Komar formulae from ADM formalism?

Is there a way to derive the Komar formulae from the ADM formulae? Both the formulae give the same answer for mass and angular momentum, so I was wondering if one can be derived from another.

On an unrelated note, if I know all the killing vectors, can I use it to uniquely determine the metric?

• if I know all the killing vectors, can I use it to uniquely determine the metric ?. I don't think this is possible. The Killing fields are defining the local symetries of the metric, but you could have two different metrics with the same symetries (for example : isotropy around a center and static spacetime). If the spacetime metric is maximally symetric, then I guess you could define the metric explicitly, but even then I'm not sure. – Cham Mar 13 '19 at 12:46
• It's generally not a good idea to ask two unrelated questions as one question on SE. I'd suggest you edit out the second one. – user4552 Mar 13 '19 at 14:28
• Even in the case where the spacetime is both asymptotically flat and stationary, it wasn't proved until 15 years after Komar that the Komar and ADM masses are equal (discussed in arxiv.org/abs/1003.5015 ). So it seems unlikely to me that it's easy to get one from the other, even in that special case. – user4552 Mar 13 '19 at 14:48