The paper investigates the singularity and extendibility of inflationary spacetimes.
problem The existence and extendibility of initial curvature singularities in inflationary spacetimes.
method Classification and rigorous extendibility criteria derivation for quasi-de Sitter spacetimes.
result Past-eternal inflationary scenarios are most likely physically singular, except in very special initial conditions.
Extends metric to Margulis spacetimes for convex properties.
problem No specific problem stated; extends metric.
method Extends Thurston's asymmetric metric to Margulis spacetimes and proves convex properties.
result Established convex properties of the extended metric.
The paper extends spacetime topology results using codimension 2 null cut locus properties.
problem Understanding spacetime topology with and without horizons.
method Review and extension of existing literature on spacetime topology, utilizing codimension 2 null cut locus properties.
result Results for spacetimes with and without horizons, including asymptotically AdS settings.
We solve the spacelike, spherically symmetric, constant mean curvature hypersurfaces in the maximally extended Reissner-Nordstrom spacetime with the charge smaller than the mass. Based on these results, we construct constant mean curvature foliations with fixed or varied mean curvature in each slice in this spacetime.
Characterizes a specific type of spacetime using vector fields.
problem Classifying a specific type of spacetime.
method Using vector fields to characterize 1+n doubly twisted spacetimes.
result Simple classification of 1+n doubly-twisted spacetimes.
Proves some flat spacetimes can't be extended smoothly.
problem Proving smooth extension of certain FLRW spacetimes.
method Utilizing Sbierski's C0-inextendibility techniques. result Proves C0-inextendibility of spatially flat FLRW spacetimes. New research proves uniqueness of maximal spacetime boundaries under certain conditions.
problem The uniqueness of maximal spacetime boundaries in extendible spacetimes.
method Analyzing manifolds with boundary, excluding specific geodesic behaviors, to prove uniqueness.
result Extendible spacetimes admit a unique maximal future boundary extension under suitable assumptions.
Extends global stability of Minkowski spacetime to minimal decay assumptions.
problem Global stability of Minkowski spacetime under minimal decay assumptions.
method Uses rp-weighted estimates instead of vectorfield method. result Proves global stability of Minkowski spacetime under minimal decay assumptions.
We introduce the notion of a standard static Finsler spacetime where the base is a Finsler manifold. We prove some results which connect causality with the Finslerian geometry of the base extending analogous ones for static and stationary Lorentzian spacetimes.
New approach confirms Kruskal-Szekeres extension for Schwarzschild spacetime.
problem Confirming the Kruskal-Szekeres extension for Schwarzschild spacetime.
method Reformulating the problem as an ODE and showing the ODE admits a solution if and only if the horizon is non-degenerate.
result Photon surfaces approaching the Killing horizon must necessarily cross it.
A generalized Robertson-Walker spacetime is the warped product with base an open interval of the real line endowed with the opposite of its metric and base any Riemannian manifold. The family of generalized Robertson-Walker spacetimes widely extends the one of classical Robertson-Walker spacetimes. In this article we p…
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.
The paper extends completeness notions to low-regularity spacetimes.
problem Defining completeness conditions for spacetimes with low-regularity metrics.
method Extending Beem's completeness notions to Lorentzian length spaces and proving relationships between them.
result Equivalence of completeness conditions for globally hyperbolic C1-spacetimes under certain conditions. We formulate the concept of time machine structure for spacetimes exhibiting a compactely constructed region with closed timelike curves. After reviewing essential properties of the pseudo Schwarzschild spacetime introduced by A. Ori, we present an analysis of its geodesics analogous to the one conducted in the case of…
Jebsen-Birkhoff theorem extended to Berwald spacetimes.
problem Generalizing Birkhoff theorem to Berwald spacetimes.
method Proving Ricci-flat, spatially spherically symmetric Berwald spacetimes are pseudo-Riemannian or flat.
result Jebsen-Birkhoff theorem extended to Berwald spacetimes.
The paper proves a spacetime positive mass theorem for singular initial data sets.
problem Proving the positive mass theorem for initial data sets with corners.
method Extending Hirsch-Kazaras-Khuri's method to singular cases using Hirsch-Miao-Tsang ideas.
result Integral lower bound on spacetime mass and characterisation of zero mass.
Spinors prove rigidity for polyhedral spacetime data.
problem Rigidity of polyhedral spacetime data sets.
method Extending rigidity analysis from spacetime positive mass theorem.
result Dihedral rigidity connects mass theorem, trapped surfaces.
We prove the existence and uniqueness of the Dirichlet problem for spacelike, spherically symmetric, constant mean curvature equation with symmetric boundary data in the extended Schwarzschild spacetime. As an application, we completely solve the CMC foliation conjecture which is posted by Malec and O Murchadha in 2003…
New proof shows FLRW spacetimes can't be extended smoothly in certain axisymmetric cases.
problem Proving smooth extension of FLRW spacetimes in specific spacetime classes.
method Extending previous work on spherically symmetric spacetimes to axisymmetric spacetimes.
result Demonstrates C0-inextendibility for FLRW spacetimes in a subclass of axisymmetric spacetimes. Extends Minkowski stability proof to minimal decay assumptions.
problem Global stability of Minkowski spacetime with minimal decay.
method Extends Christodoulou-Klainerman's proof to minimal decay assumptions.
result Exterior stability of Minkowski holds with borderline decay.
Study pp-waves with lightlike parallel spinors in vacuum spacetimes.
problem Characterize pp-waves with lightlike parallel spinors in vacuum spacetimes.
method Parametrize pp-wave spacetimes, show correspondence with Riemannian metrics, prove parallel spinor condition.
result A pp-wave spacetime with a lightlike parallel spinor corresponds to a Ricci-flat metric with a parallel spinor.
This article considers the quasi-local energy in reference to a general static spacetime. We follow the approach developed by the authors in [19, 20, 7, 9] and define the quasi-local energy as a difference of surface Hamiltonians, which are derived from the Einstein-Hilbert action. The new quasi-local energy provides a…
Study extends null distance concept to Lorentzian length spaces for spacetime analysis.
problem Understanding spacetime convergence and topology in Lorentzian geometry.
method Extend null distance concept to Lorentzian length spaces, study Gromov-Hausdorff convergence.
result First results on compatibility of null distance with synthetic curvature bounds in warped product Lorentzian length spaces.
Warped-product black hole spacetimes are C0-inextendible.
problem Future C0-inextendibility of warped-product black hole spacetimes method Adapting Sbierski's proof for a broad class of warped-product black hole spacetimes
result Future C0-inextendibility established for spacetimes with a static exterior region Let M be a globally hyperbolic maximal compact 3-dimensional spacetime locally modelled on Minkowski, anti-de Sitter or de Sitter space. It is well known that M admits a unique foliation by constant mean curvature surfaces. In this paper we extend this result to singular spacetimes with particles (cone singularit…
Chernov-Nemirovski observed that the existence of a globally hyperbolic Lorentzian metric on a (3 + 1)-spacetime pins down a smooth structure on the underlying 4-manifold. In this paper, we point out that the diffeomorphism type of a globally hyperbolic (n + 1)-spacetime is determined by the h-cobordism class of its Ca…
The paper proves that certain FLRW spacetimes cannot be extended past the big bang.
problem The singularity structure of FLRW spacetimes without particle horizons at the C0-level. method Analyzing the singularity structure of FLRW spacetimes with constant spatial curvature.
result A geometric obstruction prevents continuous spacetime extensions for a wide range of scale factors in the case of K=−1. New vacuum spacetimes without CMC Cauchy surfaces found.
problem Finding vacuum cosmological spacetimes without CMC Cauchy surfaces.
method Extended construction of [6] using spatial topologies M#M. result Obtained a large class of vacuum cosmological spacetimes.
In the present paper we provide new examples of marginally trapped surfaces and tubes in FLRW spacetimes by using a basic relation between these objects and CMC surfaces in 3-manifolds. We also provide a new method to construct marginally trapped surfaces in closed FLRW spacetimes, which is based on the classical Hopf …
Characterizes photon surfaces in static spacetimes, proving uniqueness.
problem Understanding photon surfaces in static spacetimes of arbitrary dimension.
method Complete characterization and new insights into spacetime geometry.
result Proves uniqueness of certain electrostatic spacetimes.
Extends Hopf-Rinow theorem to semi-Riemannian spacetimes.
problem Generalizing Hopf-Rinow theorem to compact Lorentzian manifolds.
method Develops null distance for proper cone structures and (n−ν,ν)-spacetimes. result Generalizes Hopf-Rinow theorem to a new class of semi-Riemannian manifolds.
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.
Analyzing static solutions in Finsler gravity, extending known results.
problem Extending the analyticity of static vacuum solutions to Finsler spacetimes.
method Examining Finsler spacetimes with properties similar to static Lorentzian spacetimes.
result Finsler spacetimes with vanishing Ricci scalar are analytic.
The paper proves a spacetime version of dihedral rigidity for cubes in 3D spacetime.
problem Proving dihedral rigidity for cubic initial data sets in 3D spacetime.
method By studying the level sets of spacetime harmonic functions and extending previous work on dihedral rigidity for prisms in hyperbolic space.
result The paper proves dihedral rigidity for cubes in 3D spacetime, extending previous results.
New findings show Berwald Finsler spacetimes cannot be metrized.
problem Can Szabo's metrizability theorem be extended to Finsler spacetimes?
method Investigation of Berwald Finsler spacetimes and their properties.
result Found a class of Berwald spacetimes with asymmetric Ricci tensors.
Researchers extend Gamma index theorem to non-compact spacetimes.
problem Establishing an L2-Gamma index for non-compact spacetimes. method Rewriting L2-Gamma index in terms of spectral flow and connecting to geometric expressions. result Extends Bär and Strohmaier's work to non-compact Cauchy hypersurfaces.
Study of charged scalar fields on Reissner-Nordström spacetimes via energy estimates.
problem Understanding the behavior and stability of charged scalar fields on near-extremal Reissner-Nordström spacetimes.
method Global integrated energy decay and boundedness estimates for solutions to the charged scalar field equation.
result Established global, weighted integrated energy decay and boundedness estimates for solutions on (near-)extremal Reissner-Nordström(--de Sitter) spacetimes.
Low regularity spacetimes split into simpler structures.
problem Proving splitting theorem for C1 metrics and weights. method Combining elliptic techniques and line-adapted curves.
result Extends Lorentzian splitting theorem to C1 settings. The paper extends gluing theorems for linearized gravitational fields in static spacetimes with cosmological constant.
problem Establishing gluing theorems for linearized vacuum gravitational fields on characteristic surfaces.
method Analyzing linearised Einstein equations in Bondi gauge on static four-dimensional spacetimes with cosmological constant.
result Generalization and extension of gluing theorems to include cosmological constant and arbitrary topology.
In this paper, we extend a technique due to Romero, Rubio and Salamanca establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed in a weighted generalized Robertson-Walker spacetime whose fiber has phi-parabolic universal Riemannian covering. As some applications of …
The Penrose theorem and Hawking's topology theorem are extended to weighted spacetimes.
problem Extending Penrose's singularity theorem and Hawking's topology theorem to weighted spacetimes.
method Using weighted null energy condition and synthetic dimension to generalize the theorems.
result Generalized versions of the Penrose and Hawking theorems hold under a weighted null energy condition.
Extends results of math-ph/0407067
Proves wave equation solutions in Kerr-de Sitter spacetime have specific asymptotic expansions.
problem Analyzing solutions to wave equations in Kerr-de Sitter spacetime.
method Developed a Fredholm setup for quasinormal modes and analyzed trapping of lightlike geodesics.
result Proves asymptotic expansions of wave equation solutions up to a decay order.
We first summarize the characterization of smooth spacelike spherically symmetric constant mean curvature (SS-CMC) hypersurfaces in the Schwarzschild spacetime and Kruskal extension. Then use the characterization to prove special SS-CMC foliation property, and verify part of the conjecture by Malec and Ó Murchadha in t…
Article strengthens initial data rigidity theorem to show unique spacetime extension.
problem Initial data rigidity in spacetime geometry.
method Showed initial data sets carry a lightlike parallel vector field, leading to unique spacetime extension.
result Local uniqueness of spacetimes extending initial data sets under dominant energy condition.
The paper extends the spacetime positive mass theorem to multiple time dimensions.
problem Proving the nonnegativity of mass in spacetimes with multiple time dimensions.
method Generalizing the spacetime positive mass theorem to include multiple time dimensions and showing mass nonnegativity through energy inequalities.
result Equality in the energy inequality implies a foliation by flat submanifolds.
The paper proves Lipschitz continuity of cut times in spacetimes.
problem Lipschitz continuity of cut times in globally hyperbolic spacetimes.
method Adapted Itoh-Tanaka method to Lorentzian setting.
result Lipschitz continuity of cut times with quantitative estimates.
Marginally outer trapped surfaces are widely considered as the best quasi-local replacements for event horizons of black holes in General Relativity. However, this equivalence is far from being proved, even in stationary and static situations. In this paper we study an important aspect of this equivalence, namely wheth…