Abstract
The Misner-Sharp-Hernandez mass defined in general relativity and in spherical symmetry has been recognized as having a Newtonian character in previous literature. In order to better understand this aspect we relax spherical symmetry and we study the generalization of the Misner-Sharp-Hernandez mass to general spacetimes, i.e., the Hawking quasilocal mass. The latter is decomposed into a matter and a pure Weyl contribution. The decomposition of the Weyl tensor into an electric part (which has a Newtonian counterpart) and a magnetic one (which does not) further splits the quasilocal mass into "Newtonian" and "non-Newtonian" parts. It is found that only the electric (Newtonian) part contributes.
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