Related papers: The spacetime positive mass theorem in dimensions …

Extending the work of Park and Strominger, we prove a positive energy theorem for the exactly solvable quantum-corrected 2D dilaton gravity theories. The positive energy functional we construct is shown to be unique (within a reasonably…

The Schwarzschild spacetime metric of negative mass is well-known to contain a naked singularity. In a spacelike slice, this singularity of the metric is characterized by the property that nearby surfaces have arbitrarily small area. We…

We prove the positive mass theorem for asymptotical flat (AF for short) manifolds with finitely many isolated conical singularities. We do not impose the spin condition. Instead we use the conformal blow up technique which dates back to…

We prove a positive volume theorem for asymptotically AdS spacetimes: the maximal volume slice has nonnegative vacuum-subtracted volume, and the vacuum-subtracted volume vanishes if and only if the spacetime is identically pure AdS. Under…

We single out a notion of staticity which applies to any domain in hyperbolic space whose boundary is a non-compact totally umbilical hypersurface. For (time-symmetric) initial data sets modeled at infinity on any of these latter examples,…

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…

We prove upper bounds on angular momentum and centre of mass in terms of the Hamiltonian mass and cosmological constant for non-singular asymptotically anti-de Sitter initial data sets satisfying the dominant energy condition. We work in…

We derive expressions for the total Hamiltonian energy of gravitating systems in higher dimensional theories in terms of the Riemann tensor, allowing a cosmological constant $\Lambda \in \mathbb{R}$. Our analysis covers asymptotically…

When a spacetime takes Bondi radiating metric, and is vacuum and asymptotically flat at spatial infinity which ensures the positive mass theorem, we prove that the standard ADM energy-momentum is the past limit of the Bondi energy-momentum.…

We extend Witten's spinor proof of the positive mass theorem to large classes of complete asymptotically flat non-spin manifolds, including all manifolds of dimension less than or equal to 11 and all manifolds of dimension less than 26…

We introduce the concept of improvability of the dominant energy scalar, and we derive strong consequences of non-improvability. In particular, we prove that a non-improvable initial data set without local symmetries must sit inside a null…

The study of stable minimal surfaces in Riemannian $3$-manifolds $(M, g)$ with non-negative scalar curvature has a rich history. In this paper, we prove rigidity of such surfaces when $(M, g)$ is asymptotically flat and has horizon…

We show how to reduce the general formulation of the mass-angular momentum inequality, for axisymmetric initial data of the Einstein equations, to the known maximal case whenever a geometrically motivated system of equations admits a…

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…

We address two problems concerning the ADM mass-minimizing initial data sets. First, we show that the equality case of the positive mass theorem embeds into a pp-wave spacetime. Second, we show that positive Bartnik mass minimizers embed…

We prove a positive mass theorem for some noncompact spin manifolds that are asymptotic to products of hyperbolic space with a compact manifold. As conclusion we show the Yamabe inequality for some noncompact manifolds which are important…

We show that extreme Myers-Perry initial data realize the unique absolute minimum of the total mass in a physically relevant (Brill) class of maximal, asymptotically flat, bi-axisymmetric initial data for the Einstein equations with fixed…

The positive mass theorem in general relativity states that in an asymptotically flat spacetime, if the momentum--energy tensor is divergence-free and satisfies a dominant energy condition, then a total momentum--energy four-vector can be…

Using the positive energy theorem, we derive some constraints on static steller models in asymptotically flat spacetimes in a general setting without imposing spherical symmetry. We show that there exist no regular solutions under certain…

W. Simon proved a conformal positive mass theorem, which was used to prove uniqueness of black holes later. In this note, we will generalize Simon's conformal positive mass theorem in two directions. First we will consider spacetime version…