Related papers: The Riemannian Penrose Inequality with Charge for …
A spherically symmetric spacetime is presented with an initial data set that is asymptotically flat, satisfies the dominant energy condition, and such that on this initial data $M<\sqrt{A/16\pi}$, where M is the total (ADM) mass and A is…
A universal geometric inequality for bodies relating energy, size, angular momentum, and charge is naturally implied by Bekenstein's entropy bounds. We establish versions of this inequality for axisymmetric bodies satisfying appropriate…
We summarize results on the Penrose inequality bounding the ADM-mass or the Bondi mass in terms of the area of an outermost apparent horizon for asymptotically flat initial data of Einstein's equations. We first recall the proof, due to…
We establish a Penrose-Like Inequality for general (not necessarily time symmetric) initial data sets of the Einstein equations which satisfy the dominant energy condition. More precisely, it is shown that the ADM energy is bounded below by…
For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the ADM mass and the area of an outermost apparent horizon, if the data are restricted suitably.…
This is the second in a series of two papers to establish the conjectured mass-angular momentum inequality for multiple black holes, modulo the extreme black hole 'no hair theorem'. More precisely it is shown that either there is a…
Penrose's original heuristic for his eponymous spacetime inequality -- a conjectured lower bound on the ADM mass in terms of the area of a horizon cross-section -- relies on the black hole final state conjecture. In this paper we isolate a…
The inequality between area and charge $A\geq 4\pi Q^2$ for dynamical black holes is proved. No symmetry assumption is made and charged matter fields are included. Extensions of this inequality are also proved for regions in the spacetime…
We show that the area-angular momentum-charge inequality (A/(4\pi))^2 \geq (2J)^2 + (Q_E^2 + Q_M^2)^2 holds for apparent horizons of electrically and magnetically charged rotating black holes in generic dynamical and non-vacuum spacetimes.…
In arXiv:0905.2622v1 and arXiv:0910.4785v1, Bray and Khuri outlined an approach to prove the Penrose inequality for general initial data sets of the Einstein equations. In this paper we extend this approach so that it may be applied to a…
We establish a Penrose-type inequality with angular momenta for four dimensional, biaxially symmetric, maximal, asymptotically flat initial data sets $(M,g,k)$ for the Einstein equations with fixed angular momenta and horizon inner boundary…
Formulation of the Penrose inequality becomes ambiguous when the past and future apparent horizons do cross. We test numerically several natural possibilities of stating the inequality in punctured and boosted single- and double- black…
We show that the Brill-Lindquist initial data provides a counterexample to a Riemannian Penrose inequality with charge conjectured by G. Gibbons. The observation illustrates a sub-additive characteristic of the area radii for the individual…
The recent holographic deduction of Penrose inequality only assumes null energy condition while the weak or dominant energy condition is required in usual geometric proof. This paper makes a step toward filling up gap between these two…
We prove the Penrose inequality with angular momentum for asymptotically flat, axisymmetric vacuum initial data sets containing a stable marginally outer trapped surface. This inequality provides a lower bound for the ADM mass in terms of…
We consider complete asymptotically flat Riemannian manifolds that are the graphs of smooth functions over $\mathbb R^n$. By recognizing the scalar curvature of such manifolds as a divergence, we express the ADM mass as an integral of the…
Consider a compact, orientable, three dimensional Riemannian manifold with boundary with nonnegative scalar curvature. Suppose its boundary is the disjoint union of two pieces: the horizon boundary and the outer boundary, where the horizon…
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 $\mathrm{ADM}$…
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…
The Penrose inequality has so far been proven in cases of spherical symmetry and in cases of zero extrinsic curvature. The next simplest case worth exploring would be non-spherical, non-rotating black holes with non-zero extrinsic…