Paper proves a rigidity result for static perfect fluids.
problem Proving a rigidity result for static perfect fluids.
method Robinson's divergence formula and boundary conditions.
result Rigidity result for static perfect fluids.
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.
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.
The paper studies Ricci solitons in perfect fluid spacetimes with specific vector fields.
problem Analyzing Ricci solitons in perfect fluid spacetimes with torse-forming vector fields.
method Examined perfect fluid spacetimes with torse-forming vector fields ξ, determined Ricci solitons, and classified their behavior as expanding, steady, or shrinking.
result Conditions for the behavior of Ricci solitons in these spacetimes were identified.
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.
Study fluid spacetimes, proving shear-free implies vanishing expansion or vorticity.
problem Understanding shear and vorticity in perfect-fluid spacetimes.
method Analyzing perfect-fluid spacetimes using Weyl tensor and divergence.
result Proves shear-free implies vanishing expansion or vorticity for perfect fluids.
New conditions for GRW space-times to be perfect-fluid space-times.
problem Conditions for GRW space-times to be perfect-fluid.
method Gray's decomposition of the gradient of the Ricci tensor, determining Ricci tensor forms in invariant subspaces.
result For most GRW space-times, the Ricci tensor is Einstein or perfect fluid.
Paper finds exact solutions for static fluids with symmetries.
problem Finding exact solutions for static fluids with symmetries.
method Utilized symmetries to solve Einstein's equation for a perfect fluid on a static manifold.
result Exact solutions found for static fluids with symmetries.
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 of k-almost Yamabe solitons in perfect fluid spacetimes.
problem Analyzing k-almost Yamabe solitons in perfect fluid spacetimes. method Examined perfect fluid spacetimes and k-almost Yamabe solitons using Einstein field equations. result Characterized properties of k-almost Yamabe solitons in perfect fluid spacetimes. The paper studies geometric structures in perfect fluid spacetimes with specific metrics.
problem Analyzing the geometric properties of perfect fluid spacetimes with specific metrics.
method Investigates conditions for conformal Ricci-Yamabe soliton and derives Laplace equations.
result Conditions for expanding, steady, or shrinking conformal Ricci-Yamabe solitons are identified.
Certain solutions of a sextic sigma-model Lagrangian reminiscent of Skyrme model correspond to perfect fluids with stiff matter equation of state. We analyse from a differential geometric perspective this correspondence extended to general barotropic fluids.
Study shows instability of naked singularities in perfect fluid models.
problem Instability of naked singularities in Einstein equations coupled with isothermal perfect fluid.
method Investigated spherically symmetric self-similar naked singularities under C1,α perturbations of an external massless scalar field. result Spherically symmetric self-similar naked singularities are unstable to trapped surface formation.
Geometrical aspects of a perfect fluid spacetime are described in terms of different curvature tensors and η-Ricci and η-Einstein solitons in a perfect fluid spacetime are determined. Conditions for the Ricci soliton to be steady, expanding or shrinking are also given. In a particular case when the potential vector…
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 …
Researchers describe the asymptotic behavior of static perfect fluids with specific equations of state.
problem Understanding the asymptotic behavior of static spherically symmetric perfect fluids with various equations of state.
method Introducing a new concept of scaled quasi-asymptotic flatness to describe the asymptotic behavior of static spherically symmetric perfect fluid solutions with linear and polytropic-type equations of state.
result The researchers provide a full geometric description of the asymptotic behavior of static spherically symmetric perfect fluid solutions with linear and polytropic-type equations of state (n>5).
Study on stellar models' topology and mass using minimal surfaces.
problem Investigating the topology and mass of static stellar models.
method Analyzing stable free boundary minimal surfaces in static perfect fluid spaces.
result Proved non-existence of stable free boundary minimal surfaces and derived upper bounds for Hawking mass.
Study kinematics of Ricci Solitons in various fluid spacetimes.
problem Understanding the motion of Ricci Solitons in different fluid spacetimes.
method Examined specific fluid spacetimes including string cloud, string fluid, etc., and analyzed kinematics.
result Obtained results and discussed physical aspects of these spacetimes.
We prove that shear-free perfect fluid solutions of Einstein's field equations must be either expansion-free or non-rotating (as conjectured by Treciokas and Ellis) for all linear equations of state p=wρ except for six values of w.
New findings on GRW space-times with constant scalar curvature.
problem Understanding GRW space-times in different subspaces.
method Analyzing orthogonal subspaces of Gray's decomposition.
result Generalized quasi-Einstein GRW space-times reduce to known types of space-times.
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 spacetimes with specific solitons in f(R)-gravity.
problem Characterizing spacetimes with specific solitons in f(R)-gravity. method Analyzing η-Ricci solitons, gradient η-Ricci solitons, gradient Einstein Solitons, and gradient m-quasi Einstein solitons in perfect fluid spacetimes obeying f(R)-gravity. result Established conditions for the behavior of η-Ricci solitons and derived significant theorems about dark matter. The paper investigates geometrical aspects of static spacetime with almost gradient Ricci solitons.
problem Geometrical properties of static spacetime with almost gradient Ricci solitons.
method Analyzing conditions and properties of static spacetime with almost gradient Ricci solitons.
result Conditions and properties of static spacetime with almost gradient Ricci solitons are determined.
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.
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.
It is expected that matter composed of a perfect fluid cannot be at rest outside of a black hole if the spacetime is asymptotically flat and static (non-rotating). However, there has not been a rigorous proof for this expectation without assuming spheical symmetry. In this paper, we provide a proof of non-existence of …
Paper finds methods to generate many Einstein solutions.
problem Finding exact solutions to Einstein's static fluid equation.
method Uses group of translations and conformal flatness to generate solutions.
result Provides an infinite number of solutions for Einstein's equation.
Characterizes Lorentzian manifolds with semi-symmetric metric connections.
problem Characterizing Lorentzian manifolds with specific metric connections.
method Analyzing semi-symmetric metric connections with vanishing curvature and recurrent torsion.
result Establishes conditions for perfect fluid and generalized Robertson-Walker spacetimes.
The paper studies φ-static perfect fluid space-times in Einstein's General Relativity.
problem Analyzing the geometry of φ-static perfect fluid space-times. method Reduction of Einstein's Field Equations to the factors of a static warped product, introducing φ-curvatures. result Sharp sufficient conditions for a compact φ-SPFST with boundary to be isometric to the standard hemisphere. 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.
In the differential geometry of certain F-structures, the role of W-curvature tensor is very well known. A detailed study of this tensor has been made on the spacetime of general relativity. The spacetimes satisfying Einstein field equations with vanishing W-tensor have been considered and the existence of Killing and …
The study calculates Weyl entropy in spacetime regions and shows its monotonic behavior.
problem Calculating and understanding Weyl entropy in spacetime regions.
method Introducing a candidate density for Weyl entropy in perfect fluid regions and analyzing its behavior in compact spacetime regions.
result Weyl entropy is shown to be monotonic in time and maximal in vacuum static metrics.
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.
Proves existence and uniqueness of rotating fluid bodies in GR to second order.
problem Understanding rotating fluid bodies in GR, especially beyond Newtonian limits.
method Second order perturbation theory, derived from first principles, with rigidly rotating finite perfect fluid ball assumptions.
result Equatorially symmetric spacetime determined by central pressure and uniform angular velocity.
This paper resolves the stiff fluid case for orthogonal Bianchi B fluids near the singularity.
problem The asymptotic behavior of orthogonal Bianchi class B stiff fluids near the initial singularity.
method Expansion-normalised variables and convergence analysis of the Jacobs set.
result All solutions converge to a specific subset of the Jacobs set, differing from non-stiff cases.
We prove theorems about the Ricci and the Weyl tensors on generalized Robertson-Walker space-times of dimension n≥3. 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…
Study on the geometry of Cotton gravity field equations.
problem Analyzing the geometry of Cotton gravity field equations.
method Describes the local structure of spatial Riemannian factors and provides sufficient conditions for reduction to φ-static perfect fluid space-time. result Provides sufficient conditions for a C-φ-PF to reduce to a φ-SPFST. We study a multiply warped products manifold associated with the Reissner-Nordstrom metric to investigate the physical properties inside the black hole event horizons. It is shown that, different from the uncharged Schwarzschild metric, the Ricci curvature components inside the Reissner-Nordstrom black hole horizons ar…
The Strong Cosmic Censorship conjecture states that for generic initial data to Einstein's field equations, the maximal globally hyperbolic development is inextendible. We prove this conjecture in the class of orthogonal Bianchi class B perfect fluids and vacuum spacetimes, by showing that unboundedness of certain curv…
The article constructs a new map for fluid dynamics and reinterprets linking numbers.
problem Understanding higher order linking numbers in fluid dynamics.
method Hydrodynamical homotopy co-momentum map and multisymplectic interpretation.
result Reinterpretation of higher order linking numbers as conserved quantities.
The paper investigates (m,ρ)-quasi-Einstein structures on almost co-Kähler manifolds.
problem Investigating (m,ρ)-quasi-Einstein structures on almost co-Kähler manifolds. method Analyzing (m,ρ)-quasi-Einstein metrics on almost co-Kähler manifolds and studying their properties. result The paper proves that (m,ρ)-quasi-Einstein structures on almost co-Kähler manifolds are rare and have specific properties. 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 P-connection is Ricci pseudo-symmetric manifold of constant type. The study characterizes special η-Ricci solitons and their harmonic properties.
problem Characterizing η-Ricci solitons with harmonic or Schrödinger-Ricci harmonic forms. method Analyzing specific cases of η-Ricci solitons using Bochner-Weitzenböck techniques. result Necessary and sufficient conditions for η to be a solution of the Schrödinger-Ricci equation. 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.
Study on stability in discretized hydrodynamics model.
problem Stability analysis of discretized hydrodynamics model.
method Geometric structure of Euler equations, convergence of sectional curvature and Jacobi equations.
result Geometric insights from discretized model transfer to Euler equations.
Study of Riemann solitons and η-hyperbolic Ricci solitons on Bochner-flat Lorentzian Kähler spacetime manifolds.
problem Analyzing soliton behaviors on Bochner-flat Lorentzian Kähler spacetime manifolds.
method Deriving explicit formulas for soliton parameters and analyzing their behaviors.
result Criteria for shrinking, steady, and expanding behaviors of solitons.
Study geometric inequalities and boundary estimates for Einstein-type manifolds with boundary.
problem Investigate geometric properties of Einstein-type manifolds with boundary.
method Investigate geometric inequalities and establish boundary estimates.
result Established boundary estimates in terms of eigenvalues and Brown-York mass.
Based on a general (1+3) threading of the spacetime (M,g), we obtain a new and simple splitting of a both the Einstein field equations (EFE) and the conservation laws in (M,g). As an application we obtain the splitting of (EFE) in an almost FLRW universe with energy-momentum tensor of a perfect fluid. In particul…