arXiv research

New relations for Penrose polynomial at n=4 and n=3.

The paper generalizes virtual knot theory using multiple types of virtual crossings.

Counterexample disproves recent Penrose conjecture variant.

Constructs homologies for ribbon graphs to recover Penrose polynomials.

Study how past eon's matter affects present eon in Penrose's cyclic cosmology.

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

Smooth metrics satisfying Penrose inequality are necessarily smooth.

We investigate the Penrose limits of classical string and M-theory backgrounds. We prove that the number of (super)symmetries of a supergravity background never decreases in the limit. We classify all the possible Penrose limits of AdS x S spacetimes and of supergravity brane solutions. We also present the Penrose limi…

Extends Penrose limit to Finsler spacetimes.

Penrose limit results for specific 3-surfaces in space-time.

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 Riemannian Penrose inequality holds in the presence of charged matter, and when …

Paper applies Newman-Penrose formalism to ACM manifolds.

New proof of Penrose inequality using potential theory.

Conditions for Penrose-Ward transformation on specific manifolds.

We propose a geometric inequality for two-dimensional spacelike surfaces in the Schwarzschild spacetime. This inequality implies the Penrose inequality for collapsing dust shells in general relativity, as proposed by Penrose and Gibbons. We prove that the inequality holds in several important cases.

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 $Ω$ extending to past null infinity. We prove a general Penrose-type inequality which involves the limit at infinity of the Hawki…

The purpose of this article is to view the Penrose kite from the perspective of symplectic geometry.

Proves existence of solutions to Einstein constraints with specific boundary conditions and verifies Penrose inequality.

The conformal flow of metrics [2] has been used to successfully establish a special case of the Penrose inequality, which yields a lower bound for the total mass of a spacetime in terms of horizon area. Here we show how to adapt the conformal flow of metrics, so that it may be applied to the Penrose inequality for gene…

Establishes a Penrose-type inequality for static spacetimes.

The Penrose-Kauffman polynomial connects knot theory to graph coloring.

Study rigidity in Penrose's singularity theorem with weakly trapped surfaces.

We establish versions of the Positive Mass and Penrose inequalities for a class of asymptotically hyperbolic hypersurfaces. In particular, under the usual dominant energy condition, we prove in all dimensions $n\geq 3$ an optimal Penrose inequality for certain graphs in hyperbolic space $\mathbb H^{n+1}$ whose boundary…

Proves Penrose inequality in all dimensions for specific manifolds.

Various complexes of differential operators are constructed on complex projective space via the Penrose transform, which also computes their cohomology.

Proves Riemannian Penrose Inequality for specific manifolds.

We prove that the Penrose limit of a spacetime along a homogeneous geodesic is a homogeneous plane wave spacetime and that the Penrose limit of a reductive homogeneous spacetime along a homogeneous geodesic is a Cahen--Wallach space. We then consider several homogenous examples to show that these results are indeed sha…

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…

Study Penrose inequality for metrics with singular sets.

We point out that algebraically special Einstein fields with twisting rays exhibit the basic properties of conformal Universes considered recently by Roger Penrose.

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…

The Riemannian Penrose inequality is a remarkable geometric inequality between the ADM mass of an asymptotically flat manifold with non-negative scalar curvature and the area of its outermost minimal surface. A version of the Riemannian Penrose inequality has also been established for the Einstein-Maxwell equations, wh…

The positive mass theorem is one of the fundamental results in general relativity. It states that, assuming the dominant energy condition, the total mass of an asymptotically flat spacetime is non-negative. The Penrose inequality provides a lower bound on mass by the area of the black hole and is closely related to the…

We study the Penrose transform for the `quaternionic objects' whose twistor spaces are complex manifolds endowed with locally complete families of embedded Riemann spheres with positive normal bundles.

Higher-dimensional Schwarzschild spacetimes violate the Penrose property.

In this paper, we show how to reduce the Penrose conjecture to the known Riemannian Penrose inequality case whenever certain geometrically motivated systems of equations can be solved. Whether or not these special systems of equations have general existence theories is therefore an important open problem. The key tool …

The paper proves a Penrose inequality for 4-discs with hyperbolic ends and conic singularities.

Researchers prove a Penrose inequality for spacetime with specific conditions.

Geometrically studies Moore-Penrose inverse and polar decomposition continuity.

Paper proves a Penrose inequality in extrinsic geometry.

The Penrose theorem and Hawking's topology theorem are extended to weighted spacetimes.

We introduce a generalized version of the Jang equation, designed for the general case of the Penrose Inequality in the setting of an asymptotically flat space-like hypersurface of a spacetime satisfying the dominat energy condition. The appropriate existence and regularity results are established in the special case o…

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.

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 …

Paper proves a generalized Penrose conjecture for flat initial data.

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 the asymptotically locally hyperbolic setting it is possible to have metrics with scalar curvature at least -6 and negative mass when the genus of the conformal boundary at infinity is positive. Using inverse mean curvature flow, we prove a Penrose inequality for these negative mass metrics. The motivation comes fro…

We extend the validity of the Penrose singularity theorem to spacetime metrics of regularity $C^{1,1}$. The proof is based on regularisation techniques, combined with recent results in low regularity causality theory.