Higher-dimensional Schwarzschild spacetimes violate the Penrose property.
problem Causal behavior of higher-dimensional Schwarzschild spacetimes.
method Analyzing causal properties in (2+1), (3+1), and (d+1) dimensions. result The Penrose property does not hold for (d+1) dimensional Schwarzschild if d>3. We extend the validity of the Penrose singularity theorem to spacetime metrics of regularity C1,1. The proof is based on regularisation techniques, combined with recent results in low regularity causality theory.
We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to the differences that arise in the Finslerian setting.
Study parallel waves in spacetimes, focusing on causality and open questions.
problem Addressing open questions in the field of parallel waves in spacetimes.
method Review and summarize existing results, introduce new concepts like null coordinates and Penrose limits.
result Progress made on the Ehlers-Kundt conjecture.
Proposes a weaker version of Strong Cosmic Censorship with curvature bounds.
problem The original Strong Cosmic Censorship conjecture.
method Weakens the conjecture to allow manifolds with bounded curvature and Lipschitz continuity of metrics.
result Proves the conjecture with bounded curvature for sufficiently large p (p>4 with uniform bounds, p>2 without uniform bounds).
Embeds spherically symmetric space-times into 5D flat space, matching Hawking temperature.
problem Finding conditions for embedding spherically symmetric space-times into flat 5D space.
method Explicitly constructs embeddings for any spherically symmetric Lorentzian metric in 3+1 dimensions.
result Hawking temperature matches Unruh temperature for Schwarzschild metric.
New metrics derived from geodesics simplify semi-Riemannian geometry.
problem Simplifying complex semi-Riemannian metrics.
method Constructing plane wave limits along geodesics.
result Generalizes Penrose's limit and encodes tensorial geometry.
We show that the Hawking--Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian metrics that are of C1,1-regularity. We formulate appropriate weak versions of the strong energy condition and genericity condition for C1,1-metrics, an…
Study shows IMP gluing spacetimes are incomplete.
problem Local geometry and completeness of IMP gluing spacetimes.
method Investigation of IMP gluing initial data sets, existence of outer trapped surfaces, and application of Penrose's incompleteness theorem.
result Implication of null incompleteness for IMP gluing spacetimes.
Study examines two topologies on future causal completion of spacetimes.
problem Characterizing differences between two topologies on future causal completion.
method Systematic examination of the stronger topology τ+ on Geroch-Kronheimer-Penrose future completion IP(X) of spacetimes X. result Complete characterization of the difference in convergence between τ+ and the weaker topology. This paper completes globally hyperbolic conformally flat spacetimes, proving they are topological manifolds.
problem Understanding the structure of spacetimes with specific properties.
method Analyzing globally hyperbolic conformally flat spacetimes, proving their causal completions are topological manifolds.
result Causal completions of globally hyperbolic conformally flat spacetimes are topological manifolds homeomorphic to S x [0, 1].
The study proves a transverse diameter theorem for Lorentzian foliations.
problem Understanding the geometry of foliations in Lorentzian spacetimes.
method Developed a novel causality structure on leaf spaces via transverse Lorentzian geometry.
result Derived a transverse diameter theorem for Lorentzian foliations and orbifolds.
Counterexample disproves recent Penrose conjecture variant.
problem A variant of the Penrose conjecture.
method Provided a counterexample.
result The conjectured variant of the Penrose inequality is false.
Constructs homologies for ribbon graphs to recover Penrose polynomials.
problem Recovering Penrose polynomials from ribbon graphs.
method TQFT-valued cube of resolutions from two-dimensional cobordisms.
result Euler characteristics of constructed homologies recover Penrose polynomials.
This paper examines the charged Riemannian Penrose inequality with and without charged matter.
problem When does the charged Riemannian Penrose inequality hold with charged matter?
method Revisited Jang's proof and constructed counterexamples to explore conditions for the inequality.
result Charged Riemannian Penrose inequality holds with suitable conditions on charged matter, but requires charge density not changing sign.
Minimal TIP and TIF found in compact spacetimes, impacting spacetime splitting.
problem Understanding the global structure of spacetimes with compact Cauchy surfaces.
method Analysis of Terminal Indecomposable Past (TIP) and Future (TIF) sets in spacetimes with compact Cauchy surfaces.
result In a spacetime with compact Cauchy surfaces, there is always at least one minimal TIP and one minimal TIF.
New relations for Penrose polynomial at n=4 and n=3.
problem Evaluation of Penrose polynomial at specific values of n.
method New ribbon graph polynomial and extended relations for n=3 to all n.
result Proven new relations for Penrose polynomial at n=4 and extended relations for n=3.
Study how past eon's matter affects present eon in Penrose's cyclic cosmology.
problem Determining present eon's matter content from past eon's matter.
method Use Penrose's reciprocity hypothesis to link past and present eons' matter.
result Perfect fluid matter content of past eon influences present eon's matter content.
Schwarzschild 3-manifold stability proven for 3D Penrose inequality.
problem Stability of the Schwarzschild 3-manifold in the context of the 3D Riemannian Penrose inequality.
method Pointed measured Gromov-Hausdorff topology, negligible domains and boundary area perturbations.
result Schwarzschild 3-manifold stability proven for 3D Penrose inequality.
Smooth metrics satisfying Penrose inequality are necessarily smooth.
problem Rigidity of Penrose inequality with singular metrics.
method Showed suitable singular metrics attaining the optimal value in the Riemannian Penrose inequality are smooth in specified coordinates.
result Smooth metrics satisfying Penrose inequality are necessarily smooth.
Study Gromov hyperbolic domains in Minkowski space, proving equivalence to boundary properties.
problem Investigate Gromov hyperbolic domains in Minkowski space.
method Explicit comparisons between metrics, dynamical arguments, and quasi-hyperbolic metric.
result Gromov hyperbolicity of convex, future complete domains is equivalent to stable acausality of the boundary.
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…
We show that when a spacetime M(=M∪∂M) is globally hyperbolic with (possibly empty) smooth timelike boundary ∂M, a metrizable topology, the closed limit topology (CLT) introduced by F. Hausdorff himself in the 1950's in set theory, can be advantageously adopted on the Geroch-Kronheime…
Extends Penrose limit to Finsler spacetimes.
problem Extending Penrose limit to Finsler spacetimes.
method Introducing lightlike coordinates and adapting Lorentzian pp-wave definition.
result New examples of Finsler pp-waves presented.
Penrose limit results for specific 3-surfaces in space-time.
problem Understanding Penrose limits for specific geometric configurations.
method Analyzing Penrose limits along null geodesics in umbilic 3-surfaces.
result Penrose limit of a specific 3-surface results in a diagonalisable plane-wave.
The Links--Gould polynomial detects causality in spacetimes.
problem Detecting causality in spacetimes using link invariants.
method Using the Links--Gould polynomial, which specializes to the Alexander--Conway polynomial.
result The Links--Gould polynomial distinguishes Allen-Swenberg links and detects causality.
Classifies and analyzes the stability of black hole event horizon birth points using contact geometry.
problem Classifying and understanding the structural possibilities of black hole crease sets.
method Contact geometry approach, focusing on BigFronts and their Legendrian projections.
result Refined stability discussion of the event horizon birth component and identification of additional components.
Paper applies Newman-Penrose formalism to ACM manifolds.
problem Classifying compact ACM manifolds with η-Einstein metrics. method Newman-Penrose formalism applied to ACM manifolds.
result Classification of compact ACM manifolds with η-Einstein metrics. New proof of Penrose inequality using potential theory.
problem Proving the Riemannian Penrose inequality for black holes.
method Establishing a monotonicity formula for the p-capacitary potential.
result A new proof of the Penrose inequality for black holes.
Conditions for Penrose-Ward transformation on specific manifolds.
problem Conditions for Penrose-Ward transformation on almost G2-manifolds with almost twistorial structures. method Necessary and sufficient conditions derived through Penrose-Ward transformation.
result Conditions for Penrose-Ward transformation on almost G2-manifolds with almost twistorial structures. 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.
Researchers prove charged Penrose inequality and positive mass theorem for specific manifold types.
problem Proving inequalities for charged initial data sets with cylindrical ends.
method Doubling argument and application of existing results by Weinstein, Yamada, and Khuri, Weinstein, Yamada.
result Established charged Penrose inequality and positive mass theorem for time symmetric initial data sets with cylindrical ends.
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 article proves charged quasi-local Penrose inequalities for compact manifolds with boundary.
problem Determining if a quasi-local version of the Riemannian Penrose inequality holds for Einstein-Maxwell equations.
method Building on ideas of Lu and Miao, and the first-named author, the article proves charged quasi-local Penrose inequalities for a class of compact manifolds with boundary.
result The lower bound on quasi-local mass is exactly the lower bound on the ADM mass given by the charged Riemannian Penrose inequality for a specific reference manifold.
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.
problem Existence of asymptotically hyperbolic solutions to Einstein constraints with marginally outer trapped boundaries.
method Constant mean curvature conformal method.
result Verification of Penrose inequality for certain Schwarzschild-AdS black hole perturbations.
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.
problem Finding a lower bound on the total mass of static spacetimes.
method Analyzes (n+1)-dimensional asymptotically flat standard static spacetimes under timelike convergence condition.
result Extends Penrose-type inequalities to all dimensions and characterizes equality conditions.
The Penrose-Kauffman polynomial connects knot theory to graph coloring.
problem Understanding the Penrose-Kauffman polynomial for cubic graphs.
method Using knot theory, the polynomial is shown equivalent to 3-coloring link diagrams.
result The Four Color Theorem is linked to 3-coloring link diagrams.
Study rigidity in Penrose's singularity theorem with weakly trapped surfaces.
problem Understand the global structure of spacetimes with weakly trapped surfaces.
method Show foliation of MOTS generating totally geodesic null hypersurfaces.
result Obtain local or global rigidity results based on assumptions.
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≥3 an optimal Penrose inequality for certain graphs in hyperbolic space Hn+1 whose boundary…
Proves Penrose inequality for specific asymptotically flat manifolds.
problem Proving Penrose inequality for certain types of manifolds.
method Developed a new approximation scheme for a flow and established monotonicity of a free boundary Hawking mass.
result Proved the Riemannian Penrose inequality for specified manifolds.
Proves Penrose inequality in all dimensions for specific manifolds.
problem Proving Penrose inequality in arbitrary dimensions for certain manifolds.
method Extends Bray's conformal-flow method to higher dimensions, dealing with singular outer-minimizing enclosures.
result Proves the Riemannian Penrose inequality in arbitrary dimensions.
Penrose conjecture proven for specific initial data sets.
problem Proving Penrose conjecture for certain types of initial data sets.
method Used σ-inverse mean curvature flow and a monotonicity formula.
result Penrose conjecture established for 2-convex initial data sets.
Proves Riemannian Penrose Inequality for specific manifolds.
problem Proving Riemannian Penrose Inequality for certain manifolds.
method Novel interplay between Hawking mass and potential-theoretic Hawking mass.
result Establishes equality between ADM mass and Huisken's Isoperimetric mass.
Various complexes of differential operators are constructed on complex projective space via the Penrose transform, which also computes their cohomology.
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…