arXiv research

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

Study on the geometry of Cotton gravity field equations.

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.

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

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

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.

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

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…

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 …

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

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

The paper examines properties of $W$-curvature tensor in relativistic space-times.

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 calculates Weyl entropy in spacetime regions and shows its monotonic behavior.

The study examines perfect fluid spacetimes and their properties.

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

Study geometric inequalities and boundary estimates for Einstein-type manifolds with boundary.

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.

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…

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.

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.

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

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.

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.

Study geometric properties of generalized vacuum static spaces.

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 $w$.

Proves a Minkowski inequality for static Einstein-Maxwell space-time.

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

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.

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

The paper classifies time-like surfaces in a static space-time.

In the framework of standard static space times, we state a family of sufficient or necessary conditions for a set of physically reasonable energy and convergence conditions in relativity and related theories. We concentrate our study on questions about the sub-harmonicity of the warping function, the scalar curvature …

Study finds conditions for certain warped product manifolds to be quasi-Einstein.

We construct a large class of new singularity-free static Lorentzian four-dimensional solutions of the vacuum Einstein equations with a negative cosmological constant. The new families of metrics contain space-times with, or without, black hole regions. Two uniqueness results are also established.

Study spherical doubly warped spacetimes for stellar collapse and cosmology.