$X$-ADM Mass and $X$-Positive Mass Theorem

Carlo Mantegazza; Francesca Oronzio

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arXiv · 2602.11372

$X$-ADM Mass and $X$-Positive Mass Theorem

Carlo Mantegazza·Francesca Oronzio

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Abstract

For a given admissible vector field $X$, we define a geometric quantity for asymptotically flat $3$--manifolds, called $X$--ADM mass and we establish a relative positive mass theorem via a monotonicity formula along the level sets of a suitable Green's function. Under different assumptions on $X$, we obtain generalizations of the ``classical'' positive mass theorem, like the one for weighted manifolds and the one ``with charge'' under some topological restrictions. Finally, we also discuss the rigidity cases.

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Carlo Mantegazza, Francesca Oronzio. 2026-02-11. $X$-ADM Mass and $X$-Positive Mass Theorem. https://arxiv.org/abs/2602.11372

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