Work

A generalization of the ADM mass for asymptotically Euclidean manifolds of weak regularity

Year: 2026

Type: article

Abstract: We propose a new definition of the ADM mass for asymptotically Euclidean manifolds inspired by the definition of mass for weakly regular asymptotically hyperbolic manifolds by Gicquaud and Sakovich. This version of the mass allows one to work with metrics of local Sobolev regularity $$ W^{1,2}_\text {loc} \cap L^\infty $$ W loc 1 , 2 ∩ L ∞ and we show, under suitable asymptotic assumptions, that the mass is finite, invariant under a change of coordinates at infinity and that it agrees with the classical ADM mass in the smooth setting. We also provide an expression in terms of the Ricci tensor that agrees with the Ricci version of the ADM mass studied by Herzlich.

Source: Geometriae Dedicata

DOI: 10.1007/s10711-025-01064-9

Authors: Stig Lundgren, Benjamin Meco

Institutions: Nagoya University, Uppsala University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,090

Funders: Ministry of Education, Culture, Sports, Science and Technology, Eberhard Karls Universität Tübingen, Uppsala Universitet, Japan Society for the Promotion of Science