arXiv research

This paper examines the charged Riemannian Penrose inequality with and without charged matter.

The article proves charged quasi-local Penrose inequalities for compact manifolds with boundary.

In this paper we investigate the extension of the charged Riemannian Penrose inequality to the case where charges are present outside the horizon. We prove a positive result when the charge densities are compactly supported, and present a counterexample when the charges extend to infinity. We also discuss additional ex…

We present a proof of the Riemannian Penrose inequality with charge $r\leq m + \sqrt{m^2-q^2}$, where $A=4πr^2$ is the area of the outermost apparent horizon with possibly multiple connected components, $m$ is the total ADM mass, and $q$ the total charge of a strongly asymptotically flat initial data set for the Einste…

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, and satisfying the relevant dominant energy condition. The proof is based on a …

This paper constructs charged Riemannian manifolds to test Penrose inequality.

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 $r=\sqrt{A/4π}$ is the area radius of $S$. A consequence of this inequality is that for connected black hole…

We reinterpret the proof of the Riemannian Penrose inequality by H. Bray. The modified argument turns out to have a nice feature so that the flow of Riemannian metrics appearing Bray's proof gives a Lorentzian metric of a spacetime. We also discuss a possible extension of our approach to charged black holes.

Researchers prove charged Penrose inequality and positive mass theorem for specific manifold types.

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 charged version of the Penrose inequality. Moreover, assuming that the initial dat…

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 connected components of an outermost horizon as a lower bound of the ADM mass.

Establishes a Penrose-type inequality for axisymmetric initial data with angular momentum and charge.

We construct a time-symmetric asymptotically flat initial data set to the Einstein-Maxwell Equations which satisfies the inequality: m - 1/2(R + Q^2/R) < 0, where m is the total mass, R=sqrt(A/4) is the area radius of the outermost horizon and Q is the total charge. This yields a counter-example to a natural extension …

We establish a Penrose-like inequality for general (not necessarily time-symmetric) initial data sets of the Einstein-Maxwell equations, which satisfy the dominant energy condition. More precisely, it is shown that the ADM energy is bounded below by an expression which is proportional to the sum of the square root of t…

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 energy conditions, thus lending credence to the most general form of Bekenstein's b…

We use the inverse mean curvature flow to establish Penrose-type inequalities for time-symmetric Einstein-Maxwell initial data sets which can be suitably embedded as a hypersurface in Euclidean space $\mathbb R^{n+1}$, $n\geq 3$. In particular, we prove a positive mass theorem for this class of charged black holes. As …

Schwarzschild 3-manifold stability proven for 3D Penrose inequality.

Smooth metrics satisfying Penrose inequality are necessarily smooth.

New proof of Penrose inequality using potential theory.

Proves Penrose inequality in all dimensions for specific manifolds.

Proves Riemannian Penrose Inequality for specific manifolds.

Establishes a Penrose-type inequality for static spacetimes.

New proof of Riemannian Penrose Inequality for manifolds with corners

The most general formulation of Penrose's inequality yields a lower bound for ADM mass in terms of the area, charge, and angular momentum of black holes. This inequality is in turn equivalent to an upper and lower bound for the area in terms of the remaining quantities. In this note, we establish the lower bound for a …

Proves Penrose inequality for specific asymptotically flat manifolds.

In a paper \cite{P} in 1973, R. Penrose made a physical argument that the total mass of a spacetime which contains black holes with event horizons of total area $A$ should be at least $\sqrt{A/16π}$. An important special case of this physical statement translates into a very beautiful mathematical inequality in Riemann…

In 1973, R. Penrose presented an argument that the total mass of a space-time which contains black holes with event horizons of total area $A$ should be at least $\sqrt{A/16π}$. An important special case of this physical statement translates into a very beautiful mathematical inequality in Riemannian geometry known as …

New proof of Riemannian Penrose inequality in 3D without horizons.

Paper proves stronger Penrose inequality with matter density.

Study on charged parallel spinors and mass-charge inequalities.

The paper establishes geometric inequalities for quasi-local masses.

Constructs fill-ins with scalar curvature lower bounds for geometric applications.

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 product of the scalar curvature and a nonnegative potential function, thus provin…

The Positive Mass Theorem states that a complete asymptotically flat manifold of nonnegative scalar curvature has nonnegative mass. The Riemannian Penrose inequality provides a sharp lower bound for the mass when black holes are present. More precisely, this lower bound is given in terms of the area of an outermost min…

This paper extends IMCF theory to Heisenberg group, solving Penrose inequality.

The Penrose inequality gives a lower bound for the total mass of a spacetime in terms of the area of suitable surfaces that represent black holes. Its validity is supported by the cosmic censorship conjecture and therefore its proof (or disproof) is an important problem in relation with gravitational collapse. The Penr…

Paper proves Penrose inequality with a weaker late-time condition.

After a detailed introduction including new examples, we give an exposition focusing on the Riemannian cases of the positive mass, Penrose, and ZAS in- equalities of general relativity, in general dimension.

New methods using spacetime harmonic functions solve geometric inequalities.

In this paper we prove a rigidity result for the equality case of the Penrose inequality on $3$-dimensional asymptotically flat manifolds with nonnegative scalar curvature and corners. Our result also has deep connections with the equality cases of Theorem 1 in \cite{Miao2} and Theorem 1.1 in \cite{LM}.

Paper proves a Penrose inequality in extrinsic geometry.

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 symmetric Riemannian manifolds with nonnegative scalar curvature whose boundaries a…

Researchers prove a Penrose inequality for spacetime with specific conditions.

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 boundary consists of the unique closed minimal surfaces in the manifold and the …

Develops a method to prove Penrose inequality for half-spaces.

The paper explores rigid geometric structures near surfaces with equality in area-charge inequalities.

The Riemannian Penrose inequality (RPI) bounds from below the ADM mass of asymptotically flat manifolds of nonnegative scalar curvature in terms of the total area of all outermost compact minimal surfaces. The general form of the RPI is currently known for manifolds of dimension up to seven. In the present work, we pro…

New mass and staticity concepts derived from weighted curvature maps.