arXiv research

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

The paper explores unique properties of Darboux transformations of spacelike curves in the Lorentz-Minkowski plane.

New invariant for special alternating links based on graph Laplacian.

In order to apply quantum topology methods to nonplanar graphs, we define a planar diagram category that describes the local topology of embeddings of graphs into surfaces. These \emph{virtual graphs} are a categorical interpretation of ribbon graphs. We describe an extension of the flow polynomial to virtual graphs, t…

Polynomials derived from Heegaard diagrams for 3-manifolds.

We analyze the horizon and geodesic structure of a class of 4D off--diagonal metrics with deformed spherical symmetries, which are exact solutions of the vacuum Einstein equations with anholonomic variables. The maximal analytic extension of the ellipsoid type metrics are constructed and the Penrose diagrams are analyz…

We introduce a differential refinement of Cohomotopy cohomology theory, defined on Penrose diagram spacetimes, whose cocycle spaces are unordered configuration spaces of points. First we prove that brane charge quantization in this differential 4-Cohomotopy theory implies intersecting p/(p+2)-brane moduli given by orde…

Counterexample disproves recent Penrose conjecture variant.

Constructs homologies for ribbon graphs to recover Penrose polynomials.

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

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.

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…

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks…

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…