Sufficient conditions for a pseudosymmetric spacetime to be a perfect fluid spacetime

The aim of this paper is to obtain the condition under which a pseudosymmetric spacetime to be a perfect fluid spacetime. It is proven that a pseudosymmetric generalized Robertson–Walker spacetime is a perfect fluid spacetime. Moreover, we establish that a conformally flat pseudosymmetric spacetime is a generalized Robertson–Walker spacetime. Next, it is shown that a pseudosymmetric dust fluid with constant scalar curvature satisfying Einstein’s field equations without cosmological constant is vacuum. Finally, we construct a nontrivial example of pseudosymmetric spacetime.

Generalized Lemaítre–Tolman–Bondi spacetime under the influence of electric charge and Palatini f(R) gravity

The objective of this article is to investigate the effects of electromagnetic field on the generalization of Lemaître–Tolman–Bondi (LTB) spacetime by keeping in view the Palatini f(R) gravity and dissipative dust fluid. For performing this analysis, we followed the strategy deployed by Herrera et al. (Phys Rev D 82(2):024021, 2010). We have explored the modified field equations along with kinematical quantities and mass function and constructed the evolution equations to study the dynamics of inhomogeneous universe along with Raychauduary and Ellis equations. We have developed the relation for Palatini f(R) scalar functions by splitting the Riemann curvature tensor orthogonally and associated them with metric coefficients using modified field equations. We have formulated these scalar functions for LTB and its generalized version, i.e., GLTB under the influence of charge. The properties of GLTB spacetime are consistent with those of the LTB geometry and the scalar functions found in both cases are comparable in the presence of charge and Palatini f(R) curvature terms. The symmetric properties of generalized LTB spacetime are also studied using streaming out and diffusion approximations.

Inhomogeneous spacetimes in Weyl integrable geometry with matter source

We investigate the existence of inhomogeneous exact solutions in Weyl Integrable theory with a matter source. In particular, we consider the existence of a dust fluid source while for the underlying geometry we assume a line element which belongs to the family of silent universes. We solve explicitly the field equations and we find the Szekeres spacetimes in Weyl Integrable theory. We show that only the isotropic family can describe inhomogeneous solutions where the LTB spacetimes are included. A detailed analysis of the dynamics of the field equations is given where the past and future attractors are determined. It is interesting that the Kasner spacetimes can be seen as past attractors for the gravitation models, while the unique future attractor describes the Milne universe similar with the behaviour of the gravitational model in the case of General Relativity.

Investigation on Computing Method of Martian Dust Fluid Based on the Energy Dissipation Method

In this paper, an initiative Martian dust fluid simulating research based on the energy dissipation method was developed to simulate the deposition process of Martian dust fluid which was caused by surface adhesion between particles and Martian rovers. Firstly, an energy dissipation model of particles based on the Discrete Element Method (DEM) was established because of the characteristics of Martian dust particles such as tiny size and viscoelasticity. This model is based on the existing DMT model to analyze the collision deposition of dust fluid particles, including particle-spacecraft collision and particle-particle collision. Secondly, this paper analyzed the characteristics of particles after their first collision, then, established the stochastic model of critical wind speed for the particle deposition process. Finally, a series of simulations of the Martian dust fluid particle deposition process were done based on DEM-CFD. The results verified the accuracy of the energy dissipation model and the stochastic model, which could also verify the feasibility and effectiveness of the computing method of Martian dust fluid based on the DEM-CFD technology.

Gravitational collapse of dust fluid and dark energy in the presence of curvature: Black hole formation

Study of gravitational collapse and black hole formation has got much interest in recent years after gravitational waves detection from mergers of black hole binaries. Here, we studied the gravitational collapse of a spherically symmetric clump of matter, constituted of dust fluid, [Formula: see text], in a background of dark energy, [Formula: see text]. We investigate the curvature effect [Formula: see text] on the gravitational collapsing process. Gravitational collapsing process for two different cases is discussed i.e. collapse of dust cloud only and collapse of dark energy. We used equation of state [Formula: see text], [Formula: see text]. For dark energy case, we discuss the collapsing process and curvature effect for different parameter values of equation of state.

Almost pseudo-Q-symmetric semi-Riemannian manifolds

The object of the present paper is to study almost pseudo-[Formula: see text]-symmetric manifolds [Formula: see text]. Some geometric properties have been studied which recover some known results of pseudo [Formula: see text]-symmetric manifolds. We obtain a necessary and sufficient condition for the [Formula: see text]-curvature tensor to be recurrent in [Formula: see text]. Also, we provide several interesting results. Among others, we prove that a Ricci symmetric [Formula: see text] is an Einstein manifold under certain condition. Moreover we deal with [Formula: see text]-flat perfect fluid, dust fluid and radiation era perfect fluid spacetimes respectively. As a consequence, we obtain some important results. Finally, we consider [Formula: see text]-spacetimes.

Enhancement of radiation on hydromagnetic Casson fluid flow towards a stretched cylinder with suspension of liquid-particles

The presence of dust particles is involved in many engineering and industrial processes like transport of petroleum, emission of smoke from vehicles, piping of power plants, treatment of wastewater, and corrosive particles in mining. Because of the importance of this phenomenon, we considered the Casson liquid flow past a stretching hollow cylinder with fluid–particle suspension and convective boundary condition aspects. Numerical solution is obtained via shooting techniques after the applying of similarity variables to the governing partial equations. Key parameters of the problem are discussed through graphs. It is noticed that the clean fluid temperature is always higher value than the dust fluid and also the presence of radiation enhanced the temperature at the surface.

Dust fluid component from Lie symmetries in scalar field cosmology

We show that in scalar field cosmology, a dust fluid follows as quantum corrections from solutions of the Wheeler–DeWitt equation generated by Lie symmetries. The energy density of the dust fluid is related with the frequency of the wave function.

LTB geometry with tilted and nontilted congruences in f(R,T) gravity

We investigate the role of tilted and nontilted congruence in the dynamics of dissipative Lemaître–Tolman–Bondi spacetime in [Formula: see text] gravity. We consider imperfect fluid with its congruences observed by tilted observer and dust fluid filled with LTB geometry observed by the nontilted observer. In order to elaborate the dynamical features of two congruences, we consider well-known [Formula: see text] models and develop relationships between tilted and nontilted dynamical variables. We evaluate the nonzero divergence of energy–momentum tensor for tilted congruence and transport equation for the system in [Formula: see text] gravity. We have also checked the instability regimes for nontilted congruence.