Recently, it is proven that generalized Robertson-Walker space-times in all orthogonal subspaces of Gray's decomposition but one(unrestricted) are perfect fluid space-times. GRW space-times in the unrestricted subspace are identified by having constant scalar curvature. Generalized quasi-Einstein GRW space-times have a…
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48 results for “GRW space-times”
We give new necessary and sufficient conditions on the Weyl tensor for generalized Robertson-Walker (GRW) space-times to be perfect-fluid space-times. For GRW space-times, we determine the form of the Ricci tensor in all the O(n)-invariant subspaces provided by Gray's decomposition of the gradient of the Ricci tensor. …
This paper explores Lorentzian manifolds with specific connections and their symmetries.
problem Characterizing Lorentzian manifolds with concircularly semi-symmetric metric connections.
method Investigates the properties of Lorentzian manifolds equipped with a concircularly semi-symmetric metric connection under specific conditions.
result Derives necessary and sufficient conditions for the manifold to be Einstein and proves that a perfect fluid space-time with a semi-symmetric metric -connection is Ricci pseudo-symmetric manifold of constant type.
We prove theorems about the Ricci and the Weyl tensors on generalized Robertson-Walker space-times of dimension . In particular, we show that the concircular vector introduced by Chen decomposes the Ricci tensor as a perfect fluid term plus a term linear in the contracted Weyl tensor. The Weyl tensor is harmoni…
The study examines a semi-symmetric metric connection in perfect fluid space-time and phantom barriers.
problem Investigating the properties of semi-symmetric metric connections in perfect fluid space-time.
method Using concircularly semi-symmetric metric connections, the study derives conditions for quasi-Einstein manifolds and examines the scalar curvature of perfect fluid space-times.
result The study proves that in a perfect fluid space-time, the scalar curvature is constant and represents a phantom barrier.
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 -quasi Einstein solitons in GRW spacetimes.
result Demonstrated that GRW spacetimes can be Robertson-Walker or phantom era spacetimes under certain conditions.
Recent work shows GRW approaches do not improve over ERM in distributional shift.
problem Improving robustness to distributional shift in machine learning models.
method Generalized Reweighting (GRW) algorithms, which iteratively update model parameters based on reweighting of training samples.
result GRW approaches do not significantly improve over ERM in real applications with distribution shift.
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.
Given two points of a Generalized Robertson-Walker spacetime, the existence, multiplicity and causal character of geodesic connecting them is characterized. Conjugate points of such geodesics are related to conjugate points of geodesics on the fiber, and Morse-type relations are obtained. Applications to bidimensional …
Generalized Robertson-Walker (GRW) spaces constitute a quite important family in Lorentzian geometry, and it is an interesting question to know whether a Lorentzian manifold can be decomposed in such a way. It is well known that the existence of a suitable vector field guaranties the local decomposition of the manifold…
Study causal structure of warped spacetimes using novel pre-length spaces.
problem Understanding the causal structure of warped spacetimes.
method Novel notion of Lorentzian pre-length spaces and proof of causal completion as globally hyperbolic pre-length space.
result Causal completion of GRW spacetime is a globally hyperbolic pre-length space under Hausdorff chronological topology.
Rigidity of spacelike hypersurfaces in spatially weighted generalized Robertson-Walker spacetimesmath.DG
Our purpose in this paper is to apply some maximum principles in order to study the rigidity of complete spacelike hypersurfaces immersed in a spatially weighted generalized Robertson-Walker (GRW) spacetime, which is supposed to obey the so called strong null convergence condition. Under natural constraints on the weig…
In this paper we study the problem of uniqueness for spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker (GRW) spacetimes. In particular, we consider the following question: Under what conditions must a compact spacelike hypersurface with constant higher order mean curvatur…
Study spherical doubly warped spacetimes for stellar collapse and cosmology.
problem Analyzing spherically symmetric spacetimes for stellar collapse and cosmology.
method Obtained results for Weyl and Ricci tensors on general doubly warped spacetimes.
result Friedmann equations deviate from standard FRW cosmology due to electric tensor terms.
The paper examines properties of -curvature tensor in relativistic space-times.
problem Investigating the properties and implications of the -curvature tensor in relativistic space-times.
method Analyzing the semi-symmetry and divergence properties of the energy-momentum tensor in relation to the -curvature tensor.
result Space-times with specific properties of the -curvature tensor are classified as Einstein or Codazzi type.
We investigate refocusing and strong refocusing of light rays in a space-time. A strongly refocusing space-time is refocusing. The converse is unknown. We construct examples of space-times which are refocusing, but not strongly so, at a particular point. These space-times are strongly refocusing at other points. The ge…
The paper examines isotropic cosmological space-times with changing sectional curvature.
problem Cosmological space-times with changing sectional curvature.
method Analysis of a family of geometrically well-behaved cosmological space-times foliated by isotropic hypersurfaces.
result Only space-time isometries ensure the rigidity properties of isotropic cosmological space-times.
New distances defined between space-times, proving some definite.
problem Defining distances between space-times.
method Introducing causal-null-compactifiable space-times and using cosmological time and null distance.
result Various definite distances defined, proving convergence of space-times.
A perfect-fluid space-time of dimension n>3 with 1) irrotational velocity vector field, 2) null divergence of the Weyl tensor, is a generalised Robertson-Walker space-time with Einstein fiber. Condition 1) is verified whenever pressure and energy density are related by an equation of state. The contraction of the Weyl …
We consider Killing vector fields on standard static space-times and obtain equations for a vector field on a standard static space-time to be Killing. We also provide a characterization of Killing vector fields on standard static space-times with compact Riemannian parts.
A large class of vacuum space-times is constructed in dimension 4+1 from hyperboloidal initial data sets which are not small perturbations of empty space data. These space-times are future geodesically complete, smooth up to their future null infinity, and extend as vacuum space-times through their Cauchy horizon. Dime…
Study Codazzi tensors in space-times, linking to Cotton gravity.
problem Understanding Codazzi tensors and their role in space-times.
method Analyzing geometric properties and proving conditions for Codazzi tensors.
result Codazzi tensors restrict space-times, influencing energy-momentum tensors in Cotton gravity.
New geometric flow equations describe how space-time dimensions change.
problem Understanding how the number of space-time dimensions affects geometry.
method Developed D-flow equations to model the variation of space-time geometries.
result Solutions for D-flow equations on D-dimensional spheres and Freund-Rubin Compactification.
The notion of maximal extension of a globally hyperbolic space-time arises from the notion of maximal solutions of the Cauchy problem associated to the Einstein's equations of general relativity. In 1969 Choquet-Bruhat and Geroch proved that if the Cauchy problem has a local solution, this solution has a unique maximal…
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 …
We investigate a generalization of the so-called metric splitting of globally hyperbolic space-times to non-smooth Lorentzian manifolds and show the existence of this metric splitting for a class of wave-type space-times. Our approach is based on smooth approximations of non-smooth space-times by families (or sequences…
New rigidity results for submanifolds in GRW spacetimes.
problem Characterizing submanifolds in GRW spacetimes.
method Maximum principles and rigidity results.
result Submanifolds must be contained in a spacelike slice.
New measure defined for Brakke flow, linking classical and new definitions.
problem Defining and characterizing the Brakke flow.
method Introduced a space-time-Grassmann measure to characterize the flow.
result Equivalence between classical and new definitions of the Brakke flow.
Study on static perfect fluid space-time geometry and boundary estimates.
problem Investigate the geometry and boundary properties of static perfect fluid space-time.
method Used generalized Reilly's formula to establish geometric inequalities and boundary estimates.
result Obtained new boundary estimates involving the Brown-York mass and first eigenvalue of the Jacobi operator.
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.
Essentially, some conditions for the Riemannian factor and the warping function of a standard static space-time are obtained in order to guarantee that no nontrivial warping function on the Riemannian factor can make the standard static space-time Einstein.
In the Minkowski space-time, a world hyper-sheet is a timelike hypersurface consisting of a one-parameter family of spacelike submanifolds. Recently, Bousso and Randall introduced the notion of caustics of world hyper-sheets in order to define the notion of holographic domains in space-time. Here, we give a mathematica…
M-CaStLe discovers causal structures in multivariate space-time data.
problem Challenges in causal graph discovery for high-dimensional gridded data.
method Generalizes CaStLe to multivariate analyses, using local embeddings and pooling spatial replicates.
result More accurately recovers multivariate causal structure and identifies physical dynamics.
In this paper, we study Ricci-flat and Einstein Lorentzian multiply warped products. We also consider the case of having constant scalar curvatures for this class of warped products. Finally, after we introduce a new class of spacetimes called as generalized Kasner space-times, we apply our results to this kind of spac…
We study constant mean curvature spacelike hypersurfaces in generalized Robertson-Walker spacetimes which are spatially parabolic covered (i.e. its fiber F is a (non- compact) complete Riemannian manifold whose universal covering is parabolic) and satisfy the null convergence condition. In particular, we provide severa…
Proves stability of Minkowski space-time for Einstein-Yang-Mills equations.
problem Stability of Minkowski space-time for perturbations governed by Einstein-Yang-Mills equations.
method Proves exterior energy estimates for tensorial non-linear wave equations in Minkowski space-time.
result Proves exterior stability of Minkowski space-time for Einstein-Yang-Mills equations.
In this paper, we investigate the null (light-like) sectional curvatures of Lorentzian warped product manifolds. We derive the formulas for the null sectional curvature of many well-known warped product space-time models such as multiply generalized Robertson-Walker space-times, generalized Kasner spacetimes and standa…
Study of Moncrief lines' behavior in curved space-times.
problem Understanding the asymptotic behavior of Moncrief lines in curved space-times.
method Analysis of geodesic laminations and convergence to Thurston boundary.
result Moncrief lines converge to a unique point in the Thurston boundary.
A study of proper affine vector fields in plane symmetric static space-times by using the rank of the Rieman matrix and holonomy. Studying proper affine vector fields in each case, It is shown that the special class of the above space-times admit proper affine vector fields.
In this paper we describe the stable and unstable leaves for the geodesic flow on the space of non-wandering spacelike geodesics of a Margulis Space Time and prove contraction properties of the leaves under the flow. We also show that monodromy of Margulis Space Times are "Anosov representations in non semi-simple Lie …
Stationary and axially symmetric space-times play an important role in astrophysics, particularly in the theory of neutron stars and black holes. The static vacuum sub-class of these space-times is known as Weyl's class, and contains the Schwarzschild space-time as its most prominent example. This paper is going to stu…
Stochastic Covariant Derivatives in a (Curved) Space-Time: a Glimpse into the Fractoid Spacesmath.PR
Study on stochastic covariant derivatives in curved space-time.
problem Analyzing covariant derivatives in curved space-time under stochastic processes.
method Using Itô-Wiener processes and stochastic calculus, including Besov spaces, Schrödinger operators, and white noise.
result Developed a framework for stochastic geodesics and white noise in fractoid spaces.
Paper develops fast, flexible Hawkes process inference for space-time data.
problem Capturing self-exciting, clustering spatio-temporal data.
method Finite support kernels, discretization, precomputations, gradient-based solver.
result Statistically accurate and fast inference for space-time Hawkes processes.
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 …
In this note we show that Lorentzian Concircular Structure manifolds (LCS)_n coincide with Generalized Robertson-Walker space-times.
Brakke flow support is parabolically rectifiable
problem Support of Brakke flow is parabolically rectifiable
method Developed approach to Brakke flow as space-time-Grassmann measure
result Standard convergence of Brakke flows is equivalent to space-time-Grassmann Radon measures
The Schroedinger operator on the Newtonian space-time is defined in a way which is independent on the class of inertial observers. In this picture the Schroedinger operator acts not on functions on the space-time but on sections of certain one-dimensional complex vector bundle over space-time. This bundle, constructed …
Sharp bounds for charged Hawking mass in electrostatic space-times.
problem Bounding charged Hawking mass in electrostatic space-times.
method Proving sharp lower bounds and upper bounds for the charged Hawking mass.
result Sharp lower bounds for the charged Hawking mass of stable surfaces in electrostatic space-times.