Related papers: Conserved quantities in General Relativity: the ca…
In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background. If the inequality is violated by an initial Cauchy data, it suggests a creation of a naked singularity, thus…
We establish a Penrose-like inequality for general (not necessarily time-symmetric) initial data sets of the Einstein-Maxwell equations, which satisfy the dominant energy condition. More precisely, it is shown that the ADM energy is bounded…
We consider Lorentzian General Relativity in a cavity with a timelike boundary, with conformal boundary conditions and also a generalization of these boundary conditions. We focus on the linearized gravitational dynamics about the static…
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…
We investigate the existence and the global causal structure of plane symmetric spacetimes with weak regularity when the matter consists of an irrotational perfect fluid with pressure equal to its mass-energy density. Our theory encompasses…
The dynamics of an M-dimensional extended object whose M+1 dimensional world volume in M+2 dimensional space-time has vanishing mean curvature is formulated in term of geometrical variables (the first and second fundamental form of the…
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.
There is a well-known short list of asymptotic conserved quantities for a physical system at spatial infinity. We search for new ones.This is carried outwithin the asymptotic framework of Ashtekar and Romano, in which spatial infinity is…
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.
Of the various energy conditions which can be assumed when studying mathematical general relativity, intuitively the simplest is the weak energy condition $\mu\geq 0$ which simply states that the observed mass-energy density must be…
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…
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…
In this short note we explain how one can use established results to prove various versions of the positive mass theorem for initial data sets with boundary, in dimensions less than 8.
Based on scale critical initial data, we construct smooth asymptotically flat Cauchy initial data for the Einstein vacuum system that does not contain Marginally Outer Trapped Surfaces (MOTS) but whose future evolution contains a trapped…
The notion of ``fundamental constant'' is heavily theory-laden. A natural, fairly precise formulation is possible in the context of the standard model (here defined to include gravity). Some fundamental constants have profound geometric…
The conformal flow of metrics [2] has been used to successfully establish a special case of the Penrose inequality, which yields a lower bound for the total mass of a spacetime in terms of horizon area. Here we show how to adapt the…
In General Relativity, finding out the geodesics of a given spacetime manifold is an important task because it determines which classical processes are dynamically forbidden. Conserved quantities play an important role in solving geodesic…
We consider versions of the Penrose singularity theorem and the Hawking horizon topology theorem in weighted spacetimes that contain weighted versions of trapped surfaces, for arbitrary spacetime dimension and synthetic dimension. We find…
General relativity can describe various gravitational systems of astrophysical relevance, like black holes and neutron stars, or even strongly coupled systems through the holographic duality. The characteristic initial (boundary) value…
Can a simple microscopic model of space and time demonstrate Special Relativity as the macroscopic (aggregate) behavior of an ensemble ? The question will be investigated in three parts. First, it is shown that the Lorentz transformation…