arXiv research

Study on static perfect fluid space-time geometry and boundary estimates.

Paper proves a rigidity result for static perfect fluids.

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. …

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 …

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…

The study examines a semi-symmetric metric connection in perfect fluid space-time and phantom barriers.

We prove theorems about the Ricci and the Weyl tensors on generalized Robertson-Walker space-times of dimension $n\ge 3$. 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…

The paper studies $\varphi$-static perfect fluid space-times in Einstein's General Relativity.

This paper aims to study the $W$-curvature tensor on relativistic space-times. The energy-momentum tensor T of a space-time is semi-symmetric given that the $W$-curvature tensor is semi-symmetric whereas energy-momentum tensor T of a space-time having a divergence free $W$-curvature tensor is of Codazzi type. A space-t…

This paper explores Lorentzian manifolds with specific connections and their symmetries.

Study on the geometry of Cotton gravity field equations.

Study Codazzi tensors in space-times, linking to Cotton gravity.

The study examines perfect fluid spacetimes and their properties.

The study examines properties of perfect fluid spacetimes in Einstein's theory.

The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.

Extended recurrent pseudo-Riemannian manifolds were introduced by Mileva Prvanovic'. We reconsider her work in the light of recent results and show that the manifold is conformally flat, and it is a space of quasi-constant curvature. We also show that an extended recurrent Lorentzian manifold, with time-like associated…

Study of $k$-almost Yamabe solitons in perfect fluid spacetimes.

The paper studies geometric structures in perfect fluid spacetimes with specific metrics.

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…

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.

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.

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.

Study on stellar models' topology and mass using minimal surfaces.

Unified method for constructing non-vacuum initial data sets in general relativity.

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 $p = w ρ$ except for six values of $w$.

The study characterizes spacetimes with specific solitons in $f(\mathcal{R})$-gravity.

The paper investigates geometrical aspects of static spacetime with almost gradient Ricci solitons.

Study how past eon's matter affects present eon in Penrose's cyclic cosmology.

The article introduces pseudo generalized Ricci-recurrent spacetimes and their applications in modified gravity.

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 …

Study spherical doubly warped spacetimes for stellar collapse and cosmology.

Characterizes Lorentzian manifolds with semi-symmetric metric connections.

We propose in this paper a new approach to the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism, and extension to higher-dimensional space-time. By considering a natural geometric definition of a matter fluid and abandoning the usual requirement of a Ricci-flat five dimension…

The study characterizes spacetime and modified gravity models using projective curvature tensor.

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.

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 paper introduces and analyzes pseudo generalized Ricci-recurrent spacetimes in modified gravity.

Proves existence and uniqueness of rotating fluid bodies in GR to second order.

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 …

In this mostly pedagogical tutorial article a brief introduction to modern geometrical treatment of fluid dynamics and electrodynamics is provided. The main technical tool is standard theory of differential forms. In fluid dynamics, the approach is based on general theory of integral invariants (due to Poincare and Car…

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.

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…