Related papers: $X$-ADM Mass and $X$-Positive Mass Theorem

There exists in General Relativity an unambiguous notion of Mass associated to asymptotically flat spacetimes known as the ADM mass. The standard expression for the same is a surface integral over spatial infinity of a linear combination of…

We give, via elementary methods, explicit formulas for the ADM mass which allow us to conclude the positive mass theorem and Penrose inequality for a class of graphical manifolds which includes, for instance, that ones with flat normal…

We derive a positive mass theorem for asymptotically flat manifolds with boundary whose mean curvature satisfies a sharp estimate involving the conformal Green's function. The theorem also holds if the conformal Green's function is replaced…

In this article, we give a proof for positive mass theorem of asymptotically flat manifolds with arbitrary ends when the dimension is no greater than seven. As an application, we also show a positive mass theorem for asymptotically locally…

On a smooth asymptotically flat Riemannian manifold with non-compact boundary, we prove a positive mass theorem for metrics which are only continuous across a compact hypersurface. As an application, we obtain a positive mass theorem on…

In this paper, a new proof of the Positive Mass Theorem is established through a newly discovered monotonicity formula, holding along the level sets of the Green's function of an asymptotically flat $3$-manifold. In the same context and for…

Motivated by the recent progress on positive mass theorem for asymptotically flat manifolds with arbitrary ends and the Gromov's definition of scalar curvature lower bound for continuous metrics, we start a program on the positive mass…

We affirm the rigidity conjecture of the spacetime positive mass theorem in dimensions less than eight. Namely, if an asymptotically flat initial data set satisfies the dominant energy condition and has $E=|P|$, then $E=|P|=0$, where $(E,…

Inspired by asymptotically flat manifolds, we introduce the concept of asymptotically flat graphs and define the discrete ADM mass on them. We formulate the discrete positive mass conjecture based on the scalar curvature in the sense of…

We study connections among the ADM mass, positive harmonic functions tending to zero at infinity, and the capacity of the boundary of asymptotically flat $3$-manifolds with nonnegative scalar curvature. First we give new formulae that…

We prove a new positive mass theorem for three-dimensional manifolds which are asymptotically hyperboloidal of order greater than $1$. The mass quantity under consideration is the volume-renormalized mass recently introduced in a paper by…

We define a generalized mass for asymptotically flat manifolds using some higher order symmetric function of the curvature tensor. This mass is non-negative when the manifold is locally conformally flat and the $\sigma_k$ curvature vanishes…

There has been a lot of interests in Positive Mass Theorems for singular metrics on smooth manifolds. We prove a positive mass theorem for asymptotically flat (AF) spin manifolds with isolated conical singularities or more generally horn…

Away from the central axis, we prove the stability of the Positive Mass Theorem in the $W^{1,p}$ sense for asymptotically flat axisymmetric manifolds with nonnegative scalar curvature satisfying some additional technical assumptions. We…

We formulate and prove the Lorentzian version of the positive mass theorems with arbitrary negative cosmological constant for asymptotically AdS spacetimes. This work is the continuation of the second author's recent work on the positive…

In this note, we consider the positive mass theorem for Riemannian manifolds $(M^{n},g)$ asymptotic to $(\mathbb{R}^{k}\times X^{n-k}, g_{\mathbb{R}^{k}}+g_{X})$ for $k\geq 3$ by studying the corresponding compactification problem.

For manifolds with a distinguished asymptotically flat end, we prove a density theorem which produces harmonic asymptotics on the distinguished end, while allowing for points of incompleteness (or negative scalar curvature) away from this…

The Positive Mass Theorem implies that any smooth, complete, asymptotically flat 3-manifold with non-negative scalar curvature which has zero total mass is isometric to (R^3, delta_{ij}). In this paper, we quantify this statement using…

We use the notion of intrinsic flat distance to address the almost rigidity of the positive mass theorem for asymptotically hyperbolic manifolds. In particular, we prove that a sequence of spherically symmetric asymptotically hyperbolic…

The positive mass theorem states that the total mass of a complete asymptotically flat manifold with non-negative scalar curvature is non-negative; moreover, the total mass equals zero if and only if the manifold is isometric to the…