Related papers: Mean-stable surfaces in Static Einstein-Maxwell th…
We prove area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory. Our inspiration comes on the one hand from a corresponding upper bound for the area in terms of the charges obtained recently by…
We derive formulas for variations of mass, angular momentum and canonical energy in Einstein (n-2)-gauge form field theory by means of the ADM formalism. Considering the initial data for the manifold with an interior boundary which has the…
We prove sharp lower bounds for the charged Hawking mass of stable surfaces in electrostatic space-times in various contexts. An upper bound for the genus of stable surfaces in the electrostatic system is provided. We also study the…
We explicitly construct static black hole solutions to the fully non-linear, D=4, Einstein-Maxwell-AdS equations that have no continuous spatial symmetries. These black holes have a smooth, topologically spherical horizon (section), but…
In this article the static Einstein-Vlasov-Maxwell system is considered in spherical symmetry. This system describes an ensemble of charged particles interacting by general relativistic gravity and Coulomb forces. First, a proof for local…
We derive inequalities between the area, the angular momentum and the charges for axisymmetric closed outermost stably marginally outer trapped surfaces, embedded in dynamical and, in general, non-axisymmetric spacetimes satisfying the…
We give a lower bound for the Lorentz length of the ADM energy-momentum vector (ADM mass) of 3-dimensional asymptotically flat initial data sets for the Einstein equations. The bound is given in terms of linear growth `spacetime harmonic…
We present a new geometric approach to the study of static isolated general relativistic systems for which we suggest the name geometrostatics. After describing the setup, we introduce localized formulas for the ADM-mass and ADM/CMC-center…
The stability and other physical properties of a class of regular black holes, quasiblack holes, and other electrically charged compact objects are investigated in the present work. The compact objects are obtained by solving the…
We explore various notions of stability for surfaces embedded and immersed in spacetimes and initial data sets. The interest in such surfaces lies in their potential to go beyond the variational techniques which often underlie the study of…
Minkowski space is shown to be globally stable as a solution to the Einstein--Vlasov system in the case when all particles have zero mass. The proof proceeds by showing that the matter must be supported in the "wave zone", and then proving…
This paper is concerned with the Klein-Gordon-Maxwell system in a bounded spatial domain. We discuss the existence of standing waves $\psi=u(x)e^{-i\omega t}$ in equilibrium with a purely electrostatic field $\mathbf{E}=-\nabla\phi(x)$. We…
We study the existence of smooth topological solitons and black strings as locally-stable saddles of the Euclidean gravitational action of five dimensional Einstein-Maxwell theory. These objects live in the Kaluza-Klein background of four…
Bounds for the area of general closed marginally trapped surfaces (MTSs) are presented. They do not require any stability condition, and are determined by a constant that depends on a particular component of the Einstein tensor on the…
We consider the problem for the classification of static and asymptotically flat Einstein-Maxwell-dilaton spacetimes with a photon sphere. It is first proven that the photon spheres in Einstein-Maxwell-dilaton gravity have constant mean and…
We show that if an asymptotically flat manifold with horizon boundary admits a global static potential, then the static potential must be zero on the boundary. We also show that if an asymptotically flat manifold with horizon boundary…
We study the stability of the Positive Mass Theorem using the Intrinsic Flat Distance. In particular we consider the class of complete asymptotically flat rotationally symmetric Riemannian manifolds with nonnegative scalar curvature and no…
The stability of a spherically symmetric self-gravitating magnetic monopole is examined in the thin wall approximation: modeling the interior false vacuum as a region of de Sitter space; the exterior as an asymptotically flat region of the…
In this study we show that, from arbitrarily dispersed initial data, both the concentration of electromagnetic fields and the focusing of gravitational waves could lead to the formation of trapped surfaces. We establish a scale-critical…
We bound the locations of outermost minimal surfaces in geometrostatic manifolds whose ADM mass is small relative to the separation between the black holes and prove the Intrinsic Flat Stability of the Positive Mass Theorem in this setting.