Related papers: Remarks on mass and angular momenta for $U(1)^2$-i…

We study, using Mean Curvature Flow methods, 2+1 dimensional cosmologies with a positive cosmological constant and matter satisfying the dominant and the strong energy conditions. If the spatial slices are compact with non-positive Euler…

This paper deals with quasi-local isoperimetric versions of the positive mass theorem on $3$-manifolds endowed with continuous complete metrics having nonnegative scalar curvature in a suitable weak sense. As a corollary, we derive…

The literature features many instances of spacetimes containing two black holes held apart by a thin distribution of matter on the axis joining the holes. For all such spacetimes, the Einstein field equations are integrated with an…

We discuss static spherically symmetric metrics which represent non-singular black holes in four- and higher-dimensional spacetime. We impose a set of restrictions, such as a regularity of the metric at the center $r=0$ and Schwarzschild…

By extending the method developed by Arav, Gauntlett, Roberts and Rosen, we construct supersymmetric $AdS_2\times{\Sigma}$ solutions of gauged $\mathcal{N}=8$ supergravity which are asymptotic to the $SU(3)\times{U}(1)$-invariant Warner…

We consider 2+1--dimensional analogues of the Bertotti-Robinson (BR) spacetimes in the sense that the coefficient at the angular part is a constant. We show that such BR-like solutions are either pure static or uncharged rotating. We trace…

In these notes we describe recent results concerning the inequality $m\geq \sqrt{|J|}$ for axially symmetric black holes.

We derive a condition under which (0,2) linear sigma models possess a ``left-moving'' conformal stress tensor in $\bq$ cohomology (i.e. which leaves invariant the ``right-moving'' ground states) even away from their critical points. At the…

Using a representation of spatial infinity based in the properties of conformal geodesics, the first terms of an expansion for the Bondi mass for the development of time symmetric, conformally flat initial data are calculated. As it is to…

Regge calculus is used to construct initial data for vacuum axisymmetric Brill waves at a moment of time symmetry. We argue that only a tetrahedral lattice can successfully reproduce the continuum solution, and develop a simplicial…

We prove positive mass theorems on ALF manifolds, i.e. complete noncompact manifolds that are asymptotic to a circle fibration over a Euclidean base, with fibers of asymptotically constant length.

A class of 2-dimensional models including 2-d dilaton gravity, spherically symmetric reduction of d-dimensional Einstein gravity and other related theories are classically analyzed. The general analytic solutions in the absence of matter…

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…

We construct initial data for several black holes with arbitrary momenta and spins by a new method that is based on a compactification of Brill-Lindquist wormholes. When treated numerically, the method leads to a significant simplification…

Near the black hole threshold in phase space, the black hole mass as a function of the initial data shows the "critical scaling" M \simeq C (p-p_*)^\gamma, where p labels a family of initial data, p_* is the value of p at the threshold, and…

We study two types of axially symmetric, stationary and asymptotically flat spacetimes using highly accurate numerical methods. The one type contains a black hole surrounded by a perfect fluid ring and the other a rigidly rotating disc of…

We prove an upper bound for angular-momentum and charge in terms of the mass for electro-vacuum asymptotically flat axisymmetric initial data sets with simply connected orbit space.

We prove a positive energy theorem in 2+1 dimensional gravity for open universes and any matter energy-momentum tensor satisfying the dominant energy condition. We consider on the space-like initial value surface a family of widening Wilson…

We prove the rigidity of positive mass theorem for asymptotically hyperbolic manifolds. Namely, if the mass equality holds, then the manifold is isometric to hyperbolic space. The result was previously proven for spin manifolds or under…

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…