Related papers: A Penrose-Like Inequality with Charge
We show how to reduce the general formulation of the mass-angular momentum inequality, for axisymmetric initial data of the Einstein equations, to the known maximal case whenever a geometrically motivated system of equations admits a…
Riemannian Penrose Inequalities are precise geometric statements that imply that the total mass of a zero second fundamental form slice of a spacetime is at least the mass contributed by the black holes, assuming that the spacetime has…
This paper investigates the geometric consequences of equality in area-charge inequalities for spherical minimal surfaces and, more generally, for marginally outer trapped surfaces (MOTS), within the framework of the Einstein-Maxwell…
It is well-known that considerations of symmetry lead to the definition of a host of conserved quantities (energy, linear momentum, center of mass, etc.) for an asymptotically flat initial data set, and a great deal of progress in…
We prove that the Riemannian Penrose Inequality holds for Asymptotically Flat $3$-manifolds with nonnegative scalar curvature and connected horizon boundary, provided the optimal decay assumptions are met, which result in the $\mathrm{ADM}$…
Stationary circularly symmetric solutions of General Relativity with negative cosmological constant coupled to the Maxwell field are analyzed in three spacetime dimensions. Taking into account that the fall-off of the fields is slower than…
We establish the positive energy theorem and a Penrose-type inequality for 3-dimensional asymptotically hyperboloidal initial data sets with toroidal infinity, weakly trapped boundary, and satisfying the dominant energy condition. In the…
This article is the sequel to our previous paper [LS] dealing with the near-equality case of the Positive Mass Theorem. We study the near-equality case of the Penrose Inequality for the class of complete asymptotically flat rotationally…
We prove that Penrose limits of metrics with arbitrary singularities of power-law type show a universal leading u^{-2}-behaviour near the singularity provided that the dominant energy condition is satisfied and not saturated. For generic…
The null Penrose inequality, i.e. the Penrose inequality in terms of the Bondi energy, is studied by introducing a funtional on surfaces and studying its properties along a null hypersurface $\Omega$ extending to past null infinity. We…
Based on the $\mu$-bubble method we are able to prove the following version of Riemannian Penrose inequality without horizon: if $g$ is a complete metric on $\mathbb R^3\setminus\{O\}$ with nonnegative scalar curvature, which is…
In this paper, we establish new area-charge inequalities for the boundary of time-symmetric Einstein-Maxwell initial data sets, in both compact and noncompact cases, under the dominant energy condition. These inequalities lead to novel…
Throughout the literature on the charged Riemannian Penrose inequality, it is generally assumed that there is no charged matter present; that is, the electric field is divergence-free. The aim of this article is to clarify when the charged…
By considering suitable axially symmetric slices on the Kruskal spacetime, we construct counterexamples to a recent version of the Penrose inequality in terms of so-called generalized apparent horizons.
Using a proper gauge condition the static spherically symmetric solutions of Einstein-Maxwell equations with charged point source at the center are derived. It is shown that the solutions of the field equations are a three-parameter family…
In this paper we prove a mass-capacity inequality and a volumetric Penrose inequality for conformally flat manifolds, in arbitrary dimensions. As a by-product of the proofs, P\'olya-Szeg\"o and Aleksandrov-Fenchel inequalities for…
We prove the existence of asymptotically hyperbolic solutions to the vacuum Einstein constraint equations with a marginally outer trapped boundary of positive mean curvature, using the constant mean curvature conformal method. As an…
Motivated by the fluid/gravity correspondence, we consider the Penrose inequality in the framework of fluid dynamics. In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background.…
In this paper, we extend the work in \cite{D}\cite{ChrusLiWe}\cite{ChrusCo}\cite{Co}. We weaken the asymptotic conditions on the second fundamental form, and we also give an $L^{6}-$norm bound for the difference between general data and…
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…