$X$-ADM Mass and $X$-Positive Mass Theorem
Differential Geometry
2026-02-13 v1
Abstract
For a given admissible vector field , we define a geometric quantity for asymptotically flat --manifolds, called --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 , 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.
Keywords
Cite
@article{arxiv.2602.11372,
title = {$X$-ADM Mass and $X$-Positive Mass Theorem},
author = {Carlo Mantegazza and Francesca Oronzio},
journal= {arXiv preprint arXiv:2602.11372},
year = {2026}
}