Related papers: Positive Energy Theorems for Spin Initial Data wit…

We establish a spacetime positive mass theorem and rigidity statement for asymptotically flat spin initial data sets with a codimension one singularity controlled by a matching Bartnik data condition involving spacetime rotations, and…

For complete spin initial data sets with an asymptotically anti--de Sitter end, we introduce a charged energy--momentum defined as a linear functional arising from the Einstein--Maxwell constraints. Under a dominant energy condition adapted…

We prove a positive mass theorem for spin initial data sets $(M,g,k)$ that contain an asymptotically flat end and a shield of dominant energy (a subset of $M$ on which the dominant energy scalar $\mu-|J|$ has a positive lower bound). In a…

We prove positive mass theorem with angular momentum and charges for axially symmetric, simply connected, maximal, complete initial data sets with two ends, one designated asymptotically flat and the other either (Kaluza-Klein)…

We establish a type of positive energy theorem for asymptotically anti-de Sitter Einstein-Maxwell initial data sets by using Witten's spinoral techniques.

We establish the positive energy theorem and a Penrose-type inequality for 3-dimensional asymptotically hyperboloidal initial data sets with toroidal infinity, weakly trapped boundary, and satisfying the dominant energy condition. In the…

In this paper we consider the positive mass theorem for general initial data sets satisfying the dominant energy condition which are singular across a piecewise smooth surface. We find jump conditions on the metric and second fundamental…

The positive energy theorem for weighted asymptotically flat spin manifolds was proved by Baldauf and Ozuch \cite{BO}, and for non-spin case by Chu and Zhu \cite{CZh}. In this paper, we generalize the positive energy theorem for…

We showed a positive energy theorem for asymptotically flat initial data sets with the concept of spectral PSC by He-Shi-Yu, Bi-Hao-He-Shi-Zhu and Brendle-Wang; and the Jang equation in Schoen-Yau, Eichmair and Jang. Then, we proved a…

We prove a harmonic asymptotics density theorem for asymptotically flat initial data sets with compact boundary that satisfy the dominant energy condition. We use this to settle the spacetime positive mass theorem, with rigidity, for…

We show a spacetime positive mass theorem for asymptotically flat initial data sets with a noncompact boundary. We develop a mass type invariant and a boundary dominant energy condition. Our proof is based on spinors.

We establish the positive energy theorem for weak asymptotically anti-de Sitter initial data sets with distributional curvature under the weak dominant energy condition.

We present a streamlined, complete proof, valid in arbitrary space dimension $n$, and using only spinors on the oriented Riemannian space $(M^{n};g),$ of the positive energy theorem in General Relativity.

In this paper, we prove the spacetime positive mass theorem for asymptotically flat spin initial data sets with arbitrary ends and a non-compact boundary. Moreover, we demonstrate a quantitative shielding theorem, subject to the tilted…

We show that the borderline cases in the proof of the positive energy theorem for initial data sets, on spin manifolds, in dimensions $n\ge 3$, are only possible for initial data arising from embeddings in Minkowski space-time.

We extend the validity of Brill's axisymmetric positive energy theorem to all asymptotically flat initial data sets with positive scalar curvature on simply connected manifolds.

A generalized positive energy theorem for spaces with asymptotic SUSY compactification involving non-symmetric data is proved. This work is motivated by the work of Dai [D1][D2], Hertog-Horowitz-Maeda [HHM], and Zhang [Z].

In this article, we revisit the initial data rigidity theorem of Eichmair, Galloway and Mendes (arxiv:2009.09527). The goal is to strengthen their result by showing that the initial data sets concerned carry a vector field that is lightlike…

We extend the positive mass theorem proved previously by the author to the Lorentzian setting. This includes the original higher dimensional positive energy theorem whose spinor proof was given by Witten in dimension four and by Xiao Zhang…

We describe a positive energy theorem for Einstein gravity coupled to scalar fields with first-derivative interactions, so-called P(X,phi) theories. We offer two independent derivations of this result. The first method introduces an…