Related papers: Spacetime positive mass theorems for initial data …
A quasi-local energy for Einstein's general relativity is defined by the value of the preferred boundary term in the covariant Hamiltonian formalism. The boundary term depends upon a choice of reference and a time-like displacement vector…
In this paper, we consider vacuum asymptotically anti-de Sitter spacetimes $( \mathscr{M}, g )$ with conformal boundary $( \mathscr{I}, \mathfrak{g} )$. We establish a correspondence, near $\mathscr{I}$, between such spacetimes and their…
We establish positive energy theorems for complete spin initial data sets with charge in dimensions $n \geq 4$, under a dominant energy condition and assuming the existence of at least one asymptotically flat end. Our results, formulated in…
We prove positivity of energy for a class of asymptotically locally hyperbolic manifolds in dimensions $4\le n \le 7$. The result is established by first proving deformation-of-mass-aspect theorems in dimensions $n\ge 4$. Our positivity…
We study connections among the ADM mass, positive harmonic functions tending to zero at infinity, and the capacity of the boundary of asymptotically flat $3$-manifolds with nonnegative scalar curvature. First we give new formulae that…
We prove that if $E$ is a compact subset of the unit disk ${\mathbb D}$ in the complex plane, if $E$ contains a sequence of distinct points $a_n\not= 0$ for $n\geq 1$ such that $\lim_{n\to\infty} a_n=0$ and for all $n$ we have $ |a_{n+1}|…
On the basis of the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a comparatively general framework for special- and general-relativistic continuum thermodynamics. In…
The study deals with a minimal energy problem in the presence of an external field over noncompact classes of vector measures of infinite dimension in a locally compact space. The components are positive measures (charges) satisfying…
We review notions of mass of asymptotically locally Anti-de Sitter three-dimensional spacetimes, and apply them to some known solutions. For two-dimensional general relativistic initial data sets the mass is not invariant under asymptotic…
We formulate and prove the Lorentzian version of the positive mass theorems with arbitrary negative cosmological constant for asymptotically AdS spacetimes. This work is the continuation of the second author's recent work on the positive…
In this article, we investigate electrostatic systems with a nonzero cosmological constant on compact manifolds with boundary. We establish new geometric properties for electrostatic manifolds in higher dimensions, extending previous…
We examine the validity of classical energy conditions in nonsingular bouncing cosmological solutions arising in quadratic curvature gravity minimally coupled to a scalar field. Focusing on the null, weak, strong, and dominant energy…
We investigate energy bounds and the stability of stationary asymptotically flat spacetimes with an ergoregion and no future horizon in the context of Einstein-Maxwell-Scalar field models which naturally arise in Kaluza-Klein and String…
In the first of two papers, we study the initial boundary-value problem that underlies the theory of the Boltzmann equation for general non-spherical hard particles. In this work, for two congruent ellipses and for a large class of…
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,…
In today's scenario, going beyond Einstein's theory of gravity leads us to some more complete and modified gravity theories. One of them is the $f(R,T)$ gravity in which $ R $ is the Ricci scalar, and $ T $ is the trace of the…
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…
In this contribution we present how to obtain explicit state space models in port-Hamiltonian form when a mixed finite element method is applied to a linear mechanical system with non-uniform boundary conditions. The key is to express the…
Shear-free or asymptotically shear-free null geodesic congruences possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant affects. It…
In this note we prove a theorem on non-vacuum initial data for general relativity. The result presents a ``rigidity phenomenon'' for the extrinsic curvature, caused by the non-positive scalar curvature. More precisely, we state that in the…