Related papers: A Penrose-Type Inequality with Angular Momentum an…
We present a proof of the Riemannian Penrose inequality with charge in the context of asymptotically flat initial data sets for the Einstein-Maxwell equations, having possibly multiple black holes with no charged matter outside the horizon,…
In this paper we revisit Brill's proof of positive mass for three-dimensional, time-symmetric, axisymmetric initial data and generalise his argument in various directions. In 3+1 dimensions, we include an apparent horizon in the initial…
In an effort to understand the Penrose inequality for black holes with angular momentum, an axisymmetric, vacuum, asymptotically Euclidean initial data set subject to certain quasi-stationary conditions is considered for a case study. A new…
We note an area-charge inequality orignially due to Gibbons: if the outermost horizon $S$ in an asymptotically flat electrovacuum initial data set is connected then $|q|\leq r$, where $q$ is the total charge and $r=\sqrt{A/4\pi}$ is the…
We prove a new geometric inequality that relates the Arnowitt-Deser-Misner mass of initial data to a quasilocal angular momentum of a marginally future trapped surface inner boundary. The inequality is expressed in terms of a 1-spinor,…
We present a formula that relates the variations of the area of extreme throat initial data with the variation of an appropriate defined mass functional. From this expression we deduce that the first variation, with fixed angular momentum,…
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…
The Penrose inequality estimates the lower bound of the mass of a black hole in terms of the area of its horizon. This bound is relatively loose for extremal or near extremal black holes. We propose a new Penrose-like inequality for static…
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…
For asymptotically flat spacetimes the Penrose inequality gives an initial data test for the weak cosmic censorship hypothesis. We give a formulation of this inequality for asymptotically anti-deSitter (AAdS) spacetimes, and show that the…
We establish the conjectured area-angular momentum-charge inequality for stable apparent horizons in the presence of a positive cosmological constant, and show that it is saturated precisely for extreme Kerr-Newman-de Sitter horizons. As…
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…
The inequality $\sqrt{J}\leq m$ is proved for vacuum, asymptotically flat, maximal and axisymmetric data close to extreme Kerr data. The physical significance of this inequality and its relation to the standard picture of the gravitational…
Let $\Omega$ be a smooth, bounded subset of $\mathbb{R}^3$ diffeomorphic to a ball. Consider $M = \mathbb{R}^3 \setminus \Omega$ equipped with an asymptotically flat metric $g = f^4 g_{\text{euc}}$, where $f\to 1$ at infinity. Assume that…
We consider initial data for extreme vacuum asymptotically flat black holes with $\mathbb{R} \times U(1)^2$ symmetry. Such geometries are critical points of a mass functional defined for a wide class of asymptotically flat, `$(t-\phi^i)$'…
Angular momentum and mass-charge inequalities for axisymmetric maximal time-symmetric initial data in Einstein-Maxwell gravity with dark matter sector were derived. The dark matter sector is mimicked by another U(1)-gauge field coupled to…
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 $\mathrm{ADM}$…
The classical Penrose inequality specifies a lower bound on the total mass in terms of the area of certain trapped surfaces. This fails at the semiclassical level. We conjecture a Quantum Penrose Inequality: the mass at spatial infinity is…
We construct initial data violating the Anti-deSitter Penrose inequality using scalars with various potentials. Since a version of the Penrose inequality can be derived from AdS/CFT, we argue that it is a new swampland condition, ruling out…
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…