Related papers: The Trautman-Bondi mass of initial data sets
We prove in this paper that, under suitable coinditions on an initial data set, we can obtain Area and Curvature Estimates for simple marginally outer trapped surfaces (or MOTS). Using this estimates, we derive a Compactness Theorem for…
We investigate the evolution of geometric invariants, as defined by Michel \cite{Michel}, in the context of asymptotically hyperboloidal initial data sets. Our focus lies on the charges of energy and linear momentum, and we study their…
The present article considers time symmetric initial data sets for the vacuum Einstein field equations which in a neighbourhood of infinity have the same massless part as that of some static initial data set. It is shown that the solutions…
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…
For a vacuum initial data set of the Einstein field equations it is possible to carry out a conformal rescaling or conformal compactification of the data giving rise to an initial data set for the Friedrich vacuum conformal equations. When…
We revisit the construction of maximal initial data on compact manifolds in vacuum with positive cosmological constant via the conformal method. We discuss, extend and apply recent results of Hebey et al. [19] and Premoselli [31] which…
We consider an infinite system of non overlapping globules undergoing Brownian motions in R^3. The term globules means that the objects we are dealing with are spherical, but with a radius which is random and time-dependent. The dynamics is…
Any compact manifold with positive scalar curvature has an associated asymptotically flat metric constructed using the Green's function of the conformal Laplacian, and the mass of this metric is an important geometric invariant. An explicit…
In this note, we consider some initial data rigidity results concerning marginally outer trapped surfaces (MOTS). As is well known, MOTS play an important role in the theory of black holes and, at the same time, are interesting spacetime…
We give a definition of mass for spacelike hypersurfaces in space-times with metrics which are asymptotic to the anti-de Sitter one, or to a class of generalizations thereof. We present the results of gr-qc/0110014 which show that our…
Newton's Second Law defines inertial mass as the ratio of the applied force on an object to the responding acceleration of the object (viz., F=ma). Objects that exhibit finite accelerations under finite forces are described as being…
We obtain restrictions on the topology of a closed connected manifold B that bounds a (possibly noncompact) manifold whose interior V admits a complete Riemannian metric of nonpositive sectional curvature. If G denotes the fundamental group…
Choosing an encoding over binary strings for input/output to/by a Turing Machine is usually straightforward and/or inessential for discrete data (like graphs), but delicate -- heavily affecting computability and even more computational…
We refine the Lyapunov-Schmidt analysis developed in our recent paper arxiv:2101.12665 to study the geometric center of mass of the asymptotic foliation by area-constrained Willmore surfaces of initial data for the Einstein field equations.…
In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a…
A deformed Bianchi type I metric in noncommutative gauge gravity is obtained. The gauge potential (tetrad fields) and scalar curvature are determined up to the second order in the noncommutativity parameters. The noncommutativity correction…
In this article, we introduce the notions of sequentially compactness and boundedly compactness in the framework of a newly defined $b_v(s)$-metric space which is a generalization of usual metric spaces and several other abstract spaces. We…
The aim of this paper is to extend some basic results about marginally outer trapped surfaces to the context of surfaces having general null expansion. Motivated in part by recent work of Chai-Wan, we introduce the notion of…
We prove a Riemannian positive mass theorem for manifolds with a single asymptotically flat end, but otherwise arbitrary other ends, which can be incomplete and contain negative scalar curvature. The incompleteness and negativity is…
In this short paper, we review recent progress on the positive mass theorem for spacelike hypersurfaces which approach to null infinity in asymptotically flat spacetimes. We use it to prove, if the functions $c(u, \theta, \psi)$, $d(u,…