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 study examines Ricci solitons and curvature inheritance on Robinson-Trautman spacetimes.
problem Investigating Ricci solitons and curvature inheritance in Robinson-Trautman spacetimes.
method Analyzing the existence of Ricci solitons and curvature inheritance properties on Robinson-Trautman spacetimes.
result Robinson-Trautman spacetimes admit various types of Ricci solitons and curvature inheritance.
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.
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 paper examines geometric properties of a unique spacetime model.
problem Investigating the geometric properties of a point-like global monopole spacetime.
method Analyzing the spacetime's pseudosymmetry structures, energy-momentum tensor, and curvature properties.
result The point-like global monopole spacetime exhibits various pseudosymmetry structures and properties.
New relation between curvature bounds and spacetime inextendibility.
problem Inextendibility of spacetimes under low regularity conditions.
method Synthetic curvature and causal character analysis.
result Low-regularity spacetimes with unbounded curvature.
New relation between curvature bounds and spacetime inextendibility.
problem Inextendibility of spacetimes under low regularity conditions.
method Synthetic curvature and causal character maximizers.
result Low-regularity inextendibility linked to unbounded curvature.
Derives spacetime regularity under specific curvature conditions.
problem Ensuring smoothness in spacetime models with given curvature constraints.
method General regularity estimate for 4-d spacetimes, using Ricci curvature and Lie derivatives.
result Establishes conditions for smoothness in spacetime models.
We prove that every (3+1)-dimensional flat GHMC Minkowski spacetime which is not a translation spacetime or a Misner spacetime carries a unique foliation by spacelike hypersurfaces of constant scalar curvature. In otherwords, we prove that every such spacetime carries a unique time function with isochrones of constan…
The paper examines geometric properties of a specific black hole spacetime.
problem Curvature properties of a Hayward black hole spacetime.
method Analyzes the curvature properties of Hayward black hole spacetime using Einstein field equations.
result The Hayward black hole spacetime is an Einstein manifold and exhibits various types of pseudosymmetry.
Study Minkowski formula for conformal Killing-Yano 2-forms in constant curvature spacetimes.
problem Derive Minkowski formula for conformal Killing-Yano 2-forms.
method Analyze spacetime Alexandrov theorem with a free boundary.
result Established spacetime Alexandrov theorem with a free boundary.
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.
Study finds limits on curvature and shape of certain spacetimes.
problem Limits on curvature and shape of compact stationary spacetimes.
method Used Petersen & Wink '21 result on Lorentzian manifolds.
result Obstructions found to curvature and topology of compact spacetimes.
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.
In this paper, we prove Lorentzian positive mass theorem for spacetimes with distributional curvature. To do so, we introduce distributional curvature and generalized Arnowitt-Deser-Misner (ADM) momentum. As an application, we discuss a junction of spacetimes.
This paper continues the investigation of constant mean curvature (CMC) time functions in maximal globally hyperbolic spatially compact spacetimes of constant sectional curvature, which was started in math.DG/0604486. In that paper, the case of flat spacetimes was considered, and in the present paper, the remaining cas…
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.
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…
Constructs constant spacetime mean curvature surfaces for hyperboloidal initial data sets.
problem Creating a foliation of constant spacetime mean curvature surfaces for asymptotically hyperboloidal initial data sets.
method Long time limit of volume preserving spacetime mean curvature flow starting from a constant mean curvature foliation.
result Obtains a foliation of constant spacetime mean curvature surfaces as the long time limit.
New method to find surfaces in null cones with constant curvature near black hole indicators.
problem Finding surfaces in null cones with constant curvature near black hole indicators.
method Flow techniques to foliate null cones by surfaces of constant spacetime mean curvature.
result A neighbourhood of stable MOTS in a null cone can be foliated by hypersurfaces of constant spacetime mean curvature.
Introduces non-regular spacetime geometry without smooth calculus.
problem Defining gravity without smooth spacetime geometry.
method Discusses non-regular spacetime geometry and curvature without differential calculus.
result Curvature and gravity can be defined without smooth spacetime calculus.
Detect spacetime curvature without rulers and clocks in 3D.
problem Detecting spacetime curvature without traditional measurement tools.
method Generalized results from 2D to 3D spacetime, proving well-stitched spacetime for conformally flat cases.
result A 3D spacetime is well-stitched if and only if it is conformally flat, providing a tool for curvature detection.
Investigates geometric properties of Bardeen black hole spacetime.
problem Examines curvature properties of Bardeen black hole spacetime.
method Analyzes pseudosymmetry, pseudosymmetric Weyl curvature, and recurrent structures.
result Bardeen spacetime is a manifold of pseudosymmetry Weyl curvature and satisfies special recurrent like structure.
Study existence of achronal hypersurfaces with prescribed mean curvature in 3D spacetimes.
problem Existence of achronal hypersurfaces with prescribed mean curvature in 3D spacetimes.
method General existence and regularity theorem for surfaces in ambient dimension 3.
result Proves existence and regularity of surfaces in 3D spacetimes.
Study generalizes submetry concept for spacetimes, linking to curvature and foliations.
problem Understanding submetry in non-positive signature spacetimes.
method Developed Lorentzian submetries and established their equivalence to semi-Riemannian submersions.
result Lorentzian submetries correspond to locally C^{1,1} semi-Riemannian submersions under completeness assumptions.
Investigates concavity of spacetimes, showing conditions for local concavity.
problem Understanding the concavity of spacetimes in Finsler geometry.
method Analyzes flag curvature and future capsules to characterize concavity.
result Berwald spacetimes are locally concave if and only if their flag curvature is nonnegative in timelike directions.
The central object of study of this thesis is inverse mean curvature vector flow of two-dimensional surfaces in four-dimensional spacetimes. Being a system of forward-backward parabolic PDEs, inverse mean curvature vector flow equation lacks a general existence theory. Our main contribution is proving that there exist …
Impact of projective curvature tensor in f(R,G), f(R,T) and f(R,Lm)-gravitygr-qc The study characterizes spacetime and modified gravity models using projective curvature tensor.
problem Characterizing spacetime and modified gravity models with projective curvature tensor.
method Analyzing $f\left(R,G
ight)$, $f\left(R,T
ight)$, and $f\left(R,L_{m}
ight)$-gravity models.
result Projectively flat perfect fluid spacetimes represent dark energy era and are locally isometric to Minkowski or de-Sitter spacetimes.
Two rigidity results for surfaces in Schwarzschild spacetime.
problem Understanding surfaces in Schwarzschild spacetime.
method Proving rigidity results for surfaces satisfying specific mean curvature equations.
result Established two new rigidity results for surfaces in Schwarzschild spacetime.
Constructs foliations of lightcones using surfaces of constant spacetime mean curvature.
problem Creating foliations of lightcones with specific geometric properties.
method Employing a geometric flow inspired by Huisken-Yau's approach for Riemannian settings.
result Initial data converges exponentially to an STCMC surface under area preserving null mean curvature flow.
Equivalence found between smooth and synthetic timelike curvature bounds.
problem Understanding timelike sectional curvature bounds in spacetime geometry.
method Established equivalence between sectional curvature bounds on timelike planes and synthetic timelike bounds.
result Equivalence proved for sectional curvature bounds on timelike planes and synthetic timelike bounds on strongly causal spacetimes.
New inequality shows all special submanifolds in light cone are totally umbilical spheres.
problem Characterizing submanifolds with parallel mean curvature in Lorentz-Minkowski spacetime.
method Established an integral inequality and used it to derive a rigidity result.
result All compact submanifolds with parallel mean curvature in light cone are totally umbilical spheres.
New CMC existence result for expanding cosmological spacetimes.
problem Establishing a new constant mean curvature (CMC) existence result for cosmological spacetimes.
method Construction of barriers in the support sense and asymptotic limit of mean curvature flow.
result The existence of a CMC Cauchy surface in expanding cosmological spacetimes.
Study geometric properties and physical applications of mixed quasi-Einstein spacetime.
problem Characterize geometric and physical properties of mixed quasi-Einstein spacetime.
method Analyze geometric conditions and curvature tensors on mixed quasi-Einstein and nearly quasi-Einstein manifolds.
result Establish conditions for specific curvature tensors and spacetime structures.
The paper proves properties of Lipschitz spacetimes with bounded Ricci curvature.
problem Properties of Lipschitz spacetimes with bounded Ricci curvature.
method Globally hyperbolic spacetimes with locally Lipschitz metrics and timelike Ricci curvature.
result New comparison theorems for Lipschitz spacetimes.
The study examines properties of perfect fluid spacetimes in Einstein's theory.
problem Analyzing curvature properties of perfect fluid spacetimes.
method Assuming perfect fluid as the source, the paper investigates solutions to Einstein's field equations.
result Properties of perfect fluid spacetimes are explored in the context of Einstein's theory.
This paper gives a new proof that maximal, globally hyperbolic, flat spacetimes of dimension n≥3 with compact Cauchy hypersurfaces are globally foliated by Cauchy hypersurfaces of constant mean curvature, and that such spacetimes admit a globally defined constant mean curvature time function precisely when they a…
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.
Som-Raychaudhuri spacetime is a stationary cylindrical symmetric solution of Einstein field equation corresponding to a charged dust distribution in rigid rotation. The main object of the present paper is to investigate the curvature restricted geometric structures admitting by the Som-Raychaudhuri spacetime and it is …
Study proves mean curvature flow in GRW spacetimes with perpendicular boundary condition.
problem Longtime existence of mean curvature flow in GRW spacetimes.
method Proved longtime existence using perpendicular Neumann boundary condition and null convergence condition.
result Metric of solution is conformal to GRW leaf's metric in asymptotic time.
The paper studies a flow of surfaces in spacetime with a focus on curvature evolution.
problem Constructing spacetime foliations and center of mass in General Relativity.
method Volume preserving curvature flow with mean curvature speed.
result The flow converges to a constant curvature limit, providing a new foliation method.
Study of prescribed mean curvature flow on noncompact hypersurfaces in Lorentz manifolds.
problem Short time existence and long time existence of prescribed mean curvature flow on noncompact spacelike hypersurfaces.
method Finding sufficient conditions for short time existence and discussing long time existence and convergence.
result Sufficient conditions for short time existence of prescribed mean curvature flow on noncompact spacelike hypersurfaces.
New findings on how conformal rescalings affect spacetime metrics.
problem Understanding how conformal rescalings impact spacetime metrics.
method Analyzing the null curvature condition and causal structure.
result Proving constraints on conformal rescalings in vacuum and non-vacuum spacetimes.
We study the geometry of stable maximal hypersurfaces in a variety of spacetimes satisfying various physically relevant curvature assumptions, for instance the Timelike Convergence Condition (TCC). We characterize stability when the target space has constant sectional curvature as well as give sufficient conditions on …
We consider open globally hyperbolic spacetimes N of dimension n+1, n≥3, which are spatially asymptotic to a Robertson-Walker spacetime or an open Friedmann universe with spatial curvature κ~=0,−1 and prove, under reasonable assumptions, that there exists a unique foliation by hypersurfaces of constant…
Paper proves uniqueness of specific spacetime surfaces in a lightcone.
problem Proving uniqueness of surfaces of constant spacetime mean curvature in a lightcone.
method Used a fairly generic notion of asymptotic flatness to prove uniqueness.
result Unique foliation by surfaces of constant spacetime mean curvature exists under weaker assumptions.
In this work we study spacelike hypersurfaces immersed in spatially open standard static spacetimes with complete spacelike slices. Under appropriate lower bounds on the Ricci curvature of the spacetime in directions tangent to the slices, we prove that every complete CMC hypersurface having either bounded hyperbolic a…
In this paper we study the r-stability of closed spacelike hypersurfaces with constant r-th mean curvature in conformally stationary spacetimes of constant sectional curvature. In this setting, we obtain a characterization of r−stability through the analysis of the first eigenvalue of an operator naturally attached…