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.
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.
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 …
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. 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.
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether solutions have finite extent (stars with a vacuum exterior) or infinite extent. In the l…
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.
In this paper we provide a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a given group of translations and whose spatial factor is conformally flat, are charac…
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.
Unified method for constructing non-vacuum initial data sets in general relativity.
problem Constructing solutions of Einstein constraint equations with coupled matter sources.
method Phase space representation and scaling of matter fields.
result Semi-decoupling of conformal constraint equations for constant-mean curvature initial data.
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.
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. 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.
In this paper geometrical aspects of perfect fluid spacetime with torse-forming vector field ξare discribed and Ricci soliton in perfect fluid spacetime with torse-forming vector field ξare determined. Conditions for the Ricci soliton to be expanding, steady or shrinking are also given.
We obtain expressions for the shear and the vorticity tensors of perfect-fluid spacetimes, in terms of the divergence of the Weyl tensor. For such spacetimes, we prove that if the gradient of the energy density is parallel to the velocity, then either the expansion rate is zero, or the vorticity vanishes. This statemen…
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. …
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…
We consider the kinematics of specific fluid spacetimes admitting timelike congruences of Ricci Solitons. These fluids includes string cloud, string fluid, perfect fluid, radially symmetric fluid, anisotropic fluid and relativistic magneto-fluid. Results are obtained and important physical aspects are discussed.
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.
In this paper we utilize symmetries in order to exhibit exact solutions to Einstein's equation of a perfect fluid on a static manifold all of whose spatial factor belongs to the conformal class of a Riemannian space of constant curvature.
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 …
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.
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.
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.
All inextendible null geodesics in four dimensional de Sitter space dS^4 are complete and globally achronal. This achronality is related to the fact that all observer horizons in dS^4 are eternal, i.e. extend from future infinity scri^+ all the way back to past infinity scri^-. We show that the property of having a nul…
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.
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.
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…
We extend the conformal gluing construction of Isenberg-Mazzeo-Pollack [18] by establishing an analogous gluing result for field theories obtained by minimally coupling Einstein's gravitational theory with matter fields. We treat classical fields such as perfect fluids and the Yang-Mills equations as well as the Einste…
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.
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.
Proves well-posedness for hard phase model in general relativity.
problem Modeling fluid dynamics in curved spacetime.
method A priori estimates and well-posedness in Sobolev spaces, coupled interior-boundary system of wave equations.
result Proves existence and uniqueness of solutions in Sobolev spaces.
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. In our previous article [Rad16], we investigated the asymptotic behaviour of orthogonal Bianchi class B perfect fluids close to the initial singularity and proved the Strong Cosmic Censorship conjecture in this setting. In several of the statements, the case of a stiff fluid had to be excluded. The present paper fills …
Study how past radiation determines present matter in Penrose's cyclic cosmology.
problem Determining matter content in the present eon from past radiation in Penrose's cyclic cosmology.
method Solve Einstein's equations for a spherical wave in the past eon, then apply reciprocity to find the present eon's matter content.
result The present eon is filled with three types of radiation: a damped wave, an in-going wave, and randomly scattered waves.
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 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. 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.
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.