Paper defines semi-quasi-Einstein manifolds and applies to Schwarzschild and Kottler spacetimes.
problem Defining and studying semi-quasi-Einstein manifolds.
method Introduced from a semi symmetric metric connection, analyzed with curvature conditions and Killing generators.
result Schwarzschild and Kottler spacetimes exhibit semi-quasi-Einstein structure.
We establish a black hole uniqueness theorem for Schwarzschild-de Sitter spacetime, also called Kottler spacetime, which satisfies Einstein's field equations of general relativity with positive cosmological constant. Our result concerns the class of static vacuum spacetimes with compact spacelike slices and regular max…
Study shows nonextendibility of warped spacelike singularities in specific spacetimes.
problem Nonextendibility of warped spacelike singularities in specific spacetimes.
method Establishes a local obstruction through integrability conditions and radial compression.
result Imply C0-inextendibility for the one-horizon Birmingham-Kottler family. Alternative proof for static black hole uniqueness with nonpositive mass.
problem Proving static uniqueness for Kottler spacetimes with nonpositive mass.
method Alternative, more elementary proof of static uniqueness theorem.
result Alternative proof of static uniqueness for Kottler spacetimes with nonpositive mass.
The paper proves energy theorems for specific initial data sets in 3D spacetime.
problem Establishing energy theorems for specific initial data sets in 3D spacetime.
method Analysis of level sets of spacetime harmonic functions.
result Rigidity results showing vanishing total energy imply isometric manifolds.
In this work, we prove an optimal Penrose inequality for asymptotically locally hyperbolic manifolds which can be realized as graphs over Kottler space. Such inequality relies heavily on an optimal weighted Alexandrov-Fenchel inequality for the mean convex star shaped hypersurfaces in Kottler space.
Researchers prove a nonlinear gluing theorem for gravitational fields near static backgrounds.
problem Proving a nonlinear gluing theorem for gravitational fields near static backgrounds.
method Proved a nonlinear characteristic Ck-gluing theorem for vacuum gravitational fields in Bondi gauge. result Generalized the C2-gluing theorem near light cones to a wider class of hypersurfaces. We present a gluing construction which adds, via a localized deformation, exactly Delaunay ends to generic metrics with constant positive scalar curvature. This provides time-symmetric initial data sets for the vacuum Einstein equations with positive cosmological constant with exactly Kottler-Schwarzschild-de Sitter en…
We construct large families of initial data sets for the vacuum Einstein equations with positive cosmological constant which contain exactly Delaunay ends; these are non-trivial initial data sets which coincide with those for the Kottler-Schwarzschild-de Sitter metrics in regions of infinite extent. From the purely Rie…
In this paper, we first study the behavior of inverse mean curvature flow in Schwarzschild manifold. We show that if the initial hypersurface Σ is strictly mean convex and star-shaped, then the flow hypersurface Σt converges to a large coordinate sphere as t→∞ exponentially. We also describe an a…
New static black hole uniqueness theorems for negative cosmological constant.
problem Uniqueness of static black holes in asymptotically locally hyperbolic spaces.
method Inequality relating surface gravity and topology, rigidity of Kottler black holes, monotone quantities under IMCF, regularity theorem for IMCF.
result Static black holes are uniquely determined by their geometry and topology.
We prove that the TT-gauge-fixed linearised Einstein operator is non-degenerate for Riemannian Kottler ("Schwarzschild-anti de Sitter") metrics with dimension- and topology-dependent ranges of mass parameter. We provide evidence that this remains true for all such metrics except the spherical ones with a critical mas…
We prove Birkhoff-type results showing that L2 solutions of the linearized Einstein equations around Riemannian Kottler ("Schwarzschild-anti de Sitter") metrics in arbitrary dimension and horizon topology, which are not controlled by "master functions" are pure gauge. Together with earlier results this implies that …
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…
Building upon the work of Brendle, Marques and Neves on the construction of counterexamples to Min-Oo's conjecture, we exhibit deformations of the de Sitter-Schwarzschild space of dimension n≥3 satisfying the dominant energy condition and agreeing with the standard metric along the event and cosmological horizons…
The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.
problem Characterizing pseudosymmetric spacetimes as perfect fluids.
method Analyzes generalized Robertson-Walker spacetimes, conformally flat spacetimes, and dust fluids.
result Conditions for pseudosymmetric spacetimes to be perfect fluids are established.
We consider (flat) Cauchy-complete GH spacetimes, i.e., globally hyperbolic flat lorentzian manifolds admitting some Cauchy hypersurface on which the ambient lorentzian metric restricts as a complete riemannian metric. We define a family of such spacetimes - model spacetimes - including four subfamilies: translation sp…
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 introduces and analyzes pseudo generalized Ricci-recurrent spacetimes in modified gravity.
problem Characterizing and analyzing pseudo generalized Ricci-recurrent spacetimes in modified gravity.
method Introducing and characterizing pseudo generalized Ricci-recurrent spacetimes, proving their properties, and studying their impact under modified gravity scenarios.
result Pseudo generalized Ricci-recurrent spacetimes represent specific spacetime types under modified gravity scenarios.
The study characterizes spacetimes with quasi-constant sectional curvature and explores their properties in F(R)-gravity.
problem Characterizing spacetimes with quasi-constant sectional curvature.
method Investigation through examples, proofs, and analysis of energy conditions.
result A spacetime of quasi-constant sectional curvature can represent a Robertson Walker spacetime or a static spacetime.
The article introduces pseudo generalized Ricci-recurrent spacetimes and their applications in modified gravity.
problem Characterizing and understanding pseudo generalized Ricci-recurrent spacetimes.
method Introduced and characterized pseudo generalized Ricci-recurrent spacetimes, provided examples, and studied their implications in modified gravity.
result Pseudo generalized Ricci-recurrent spacetimes represent perfect fluid spacetimes and can model dark energy epochs or static spacetimes.
The paper studies the past inextendibility of FLRW spacetimes using the VDR asymptote.
problem Investigating the past inextendibility of FLRW spacetimes.
method Using the volume-distance-ratio (VDR) asymptote to assess spacetime inextendibility criteria.
result Conditions for past inextendibility of FLRW spacetimes are identified.
Study explores geometric properties of Vaidya-Bonner-de Sitter spacetime.
problem Exploring geometric properties of Vaidya-Bonner-de Sitter spacetime.
method Analyzing conformal curvature, conharmonic curvature, and other curvatures.
result VBdS spacetime exhibits various pseudosymmetric structures and geometric features.
The study characterizes GRW spacetimes with gradient solitons and phantom era.
problem Characterizing generalized Robertson-Walker spacetimes with gradient solitons.
method Examined gradient type Ricci solitons and (m,τ)-quasi Einstein solitons in GRW spacetimes. result Demonstrated that GRW spacetimes can be Robertson-Walker or phantom era spacetimes under certain conditions.
Characterizes Lorentzian manifolds embeddable in Minkowski spacetime.
problem Identifying Lorentzian manifolds embeddable in Minkowski spacetime.
method Characterization and proof of embeddability conditions.
result Lorentzian manifolds embeddable in Minkowski spacetime coincide with globally hyperbolic spacetimes.
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. Study of quasilocal mass using isometric embedding in various spacetimes.
problem Understanding quasilocal mass in different spacetimes.
method Application of isometric embedding theory to quasilocal mass.
result Recent progress in quasilocal mass calculations with specific spacetimes.
Characterizes pseudo B-symmetric spacetimes and their implications in f(R) gravity.
problem Characterizing pseudo B-symmetric spacetimes and their properties.
method Analyzes Codazzi type of B-tensor and applies f(R) gravity model.
result Pseudo B-symmetric spacetimes with Codazzi type B-tensor are conformally flat and Robertson-Walker spacetimes.
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.
Study maximal hypersurfaces in open spacetimes using a maximum principle.
problem Characterize maximal hypersurfaces in open spacetimes.
method Use a generalized maximum principle to analyze hypersurfaces in spatially open Generalized Robertson-Walker spacetimes.
result Provide new uniqueness and non-existence results for complete maximal hypersurfaces in open Robertson-Walker spacetimes.
The study explores properties of a specific type of spacetime.
problem Discussing geometric and physical properties of hyper-generalised quasi-Einstein spacetime.
method Analyzing various types of pseudosymmetry and Ricci symmetry over the spacetime.
result Proved the existence of a non-trivial hyper-generalised quasi-Einstein spacetime.
New findings show cosmological constant as initial condition for non-isotropic spacetimes.
problem Cosmological constant as initial condition in non-isotropic spacetimes.
method Generalized previous results to non-isotropic spacetimes.
result Quasi de Sitter expansion for early universe, potential for inflationary scenarios.
We consider the class of locally boost isotropic spacetimes in arbitrary dimension. For any spacetime with boost isotropy, the corresponding curvature tensor and all of its covariant derivatives must be simultaneously of alignment type D relative to some common null frame. Such spacetimes are known as type ${\b…
Study finds unique and non-existent constant mean curvature hypersurfaces in specific spacetimes.
problem Finding unique and non-existent constant mean curvature spacelike hypersurfaces.
method Geometric and physical assumptions applied to Generalized Robertson-Walker spacetimes.
result New uniqueness and non-existence results for complete spacelike hypersurfaces.
New Galilean spacetimes found as pp-wave reductions.
problem Understanding isotropic homogeneous Galilean spacetimes.
method Null reductions of pp-wave spacetimes.
result Found novel torsional Galilean spacetimes.
Study revisits Bondi mass and discusses memory effect in polyhomogeneous spacetimes.
problem Analyzing the asymptotic behavior and memory effect in polyhomogeneous spacetimes.
method Revisits Bondi mass using Iyer-Wald formalism and discusses memory effect in vacuum polyhomogeneous spacetimes.
result The balance law remains unchanged in polyhomogeneous spacetimes with logarithmic terms.
Study baryogenesis in conformally flat spacetimes using causal fermion systems.
problem Understanding baryogenesis in specific spacetimes.
method Analysis of baryogenesis mechanism in conformally flat spacetimes with explicit formula derivation.
result Explicit formula for baryogenesis rate in these spacetimes.
In 2+1 dimensions, all complete spacetimes are cylindrical.
problem Understanding rigidity of Ricci flow spacetimes in (2+1) dimensions. method Analyzing complete and sufficiently regular spacetimes, showing they must be cylindrical.
result Every spatial slice is diffeomorphic to a fixed surface, and the spacetime is isometric to a classical Ricci flow.
The study examines perfect fluid spacetimes and their properties.
problem Characterizing properties of perfect fluid spacetimes with concircular vector fields.
method Analyzing the conformal curvature tensor, state equation, and solitons in perfect fluid spacetimes.
result Perfect fluid spacetimes with concircular vector fields have specific properties related to the state equation and solitons.
Causal spacetimes with Ricci tensor have unique transformations.
problem Understanding transformations in viable causal spacetimes.
method Analyzing Ricci tensor and causal diffeomorphisms.
result Causal diffeomorphisms preserving Ricci tensor are homotheties.
Milne-like spacetimes are a class of FLRW models which admit C0 spacetime extensions through the big bang. The boundary of a Milne-like spacetime can be identified with a null cone in the extension. We find that the comoving observers all emanate from a single point in the extension. This suggests that something phy…
Detect spacetime curvature with event causality measurements.
problem Detecting spacetime curvature without rulers and clocks.
method Prove spacetime non-flatness through causal relations.
result Sixteen measurements verify non-flatness of non-conformally flat spacetimes.
The Levi-Civita connection and geodesic equations for a stationary spacetime are studied in depth. General formulae which generalize those for warped products are obtained. These results are applicated to some regions of Kerr spacetime previously studied by using variational methods. We show that they are neither space…
This study proves energy bounds in specific AdS spacetimes.
problem Proving positive energy theorems in asymptotically locally AdS spacetimes.
method Derived positive energy theorem for spacetimes with compact, Einstein cross-sections.
result First complete proofs of BPS inequalities in AdS and locally AdS spacetimes.
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…
Researchers found differential invariants for Kundt spacetimes.
problem Equivalence problem for Lorentzian metrics in Kundt spacetimes.
method Found generators for rational differential invariants for Kundt spacetimes.
result Relating findings to other approaches to the equivalence problem.
Classifies Lie algebras and related spacetimes for a specific type of symmetry.
problem Classifying Lie algebras and related spacetimes for a specific type of symmetry.
method Classification of Lie algebras, homogeneous spacetimes, and coadjoint orbits.
result Classification of three types of Lifshitz spacetimes.
No closed timelike geodesics in Kerr spacetimes, proving absence of closed causal geodesics.
problem Proving the nonexistence of closed timelike geodesics in Kerr spacetimes.
method Analyzing the Kerr-star spacetime, excluding closed null geodesics and proving the nonexistence of closed timelike geodesics.
result No closed timelike geodesics in Kerr spacetimes.