Narrow Results

The concept of dark matter (DM) hypothesis comes out as a result from the input of the observed flat rotational velocity. With the assumption that the galactic halo is pseudo-spheroidal and filled with charged perfect fluid, we have obtained a solution which has inkling to a (nearly) flat universe, compatible with the modern day cosmological observations. Various other important aspects of the solution such as attractive gravity in the halo region and the stability of the circular orbit are also explored. Also, the matter in the halo region satisfies the known equation of state which indicates its non-exotic nature.

The field equations within the framework of Lyra's geometry with a time-dependent displacement vector field for a Bianchi type-V space–time filled with a perfect fluid and heat flow are presented. Two different classes of physically viable solutions are obtained by using a special law of variation for the generalized mean Hubble's parameter which correspond to singular and nonsingular models with constant deceleration parameter. These models are found to be consistent with the observations on the present day universe. Some thermodynamical relations are studied. The physical and kinematical behaviors of the models are also discussed.

In this paper, we analyze the wormhole solutions in $f(R)$ gravity. Specifically we sought for wormhole geometry solutions for the following three shape functions: (i) $b(r)=r_0+{\rho }_0{r}_0^{3}ln\left(\frac{r_0}{r}\right)$, (ii) $b(r)=r_0+\gamma r_0\left(1-\frac{r_0}{r}\right)$ and (iii) $b(r)=\alpha +\beta r$, under some legitimate physical conditions on the parameters as well as constants involved here with the shape functions. It is observed from the graphical plots that the behavior of the physical parameters are interesting and viable.

In this paper, we have investigated the physical behavior of cosmological models in the framework of modified teleparallel gravity. This model is established using a Rényi holographic dark energy (RHDE) model with a Hubble cut-off. Here, we have considered a homogeneous and isotropic Friedman universe filled with perfect fluid. The physical parameters are derived for the present model in compliances with 43 observational Hubble data sets. The equation-of-state parameter in terms of $H(z)$ describes the transition of the universe between phantom and nonphantom phases in the context of $f(T)$ gravity. Our model shows the violation of strong energy condition and the weak energy condition over the accelerated phantom regime. We also observed that these models occupy freezing regions through ${\omega }_D$–${\omega }_D^{\prime }$ plane. Consequently, our RHDE model is supported to the consequences of general relativity in the framework of $f(T)$ modified gravity.

In this paper, we present the construction and analysis of an interior solution for a compact star in Rastall gravity. The space–time considered is static and spherically symmetric, meanwhile, the source of matter is that of a perfect fluid. The solution of the equations system which describes the model is obtained from a specific form of the red shift factor function and its result is physically acceptable. The analysis of the solution is focused on the description of the star PSR $\mathrm{\text{J}}0348+0432$, for which we know the observational data of mass $M=(2.01\pm 0.04)M_{\odot }$ and radius $R=(12.5095\pm 0.4475)$km, a comparison with the behavior of the solution in the frame of Einstein’s general relativity theory, $\lambda =1$, shows that for $\lambda >1$ the density, pressure and speed of sound are greater, meanwhile for $\lambda <1$ their values are lower. The analysis of the generalized TOV equation to the case of the Rastall gravity implies that the contribution of the force associated to the Rastall parameter can generate an attractive ($\lambda >1$) or repulsive ($\lambda <1$) force, showing the relevance and the effect that the Rastall parameter has in stellar models.

We consider an Anti-de Sitter universe filled by quantum conformal matter with the contribution from the usual tachyon and a perfect fluid. The model represents the combination of a trace-anomaly annihilated and a tachyon driven Anti-de Sitter universe. The influence exerted by the quantum effects and by the tachyon on the AdS space is studied. The radius corresponding to this universe is calculated and the effect of the tachyon potential is discussed, in particular, concerning the possibility to get an accelerated scale factor for the proposed model (which yields an accelerated expansion of the AdS type of universe). Fulfillment of the cosmological energy conditions in the model is also investigated.

Self-similar solutions of a collapsing perfect fluid and a massless scalar field with kinematic self-similarity of the second kind in (2 + 1) dimensions are obtained. The local and global properties of the solutions are studied. It is found that some of them represent gravitational collapse, in which black holes are always formed, and some may be interpreted as representing cosmological models.

In this work, the gravitational collapse of an inhomogeneous spherical star model, consisting of inhomogeneous dust in the background of perfect fluid or anisotropic fluid, is considered. The process of collapse is first examined separately for the dust and perfect fluid, and then under their combined effect, with or without interaction, for both marginally and nonmarginally bound cases. Finally, collapsing matter in the form of anisotropic fluid is investigated and it is found to be similar to that in the study by Chakraborty et al. (2005).

Considering the standard "static" spherically symmetric ansatz ds² = −B(r) dt² + A(r) dr² + r² dΩ² for Einstein's equations with perfect fluid source, we ask how we can interpret solutions where A(r)andB(r) are not positive, as they must be for the static matter source interpretation to be valid.

Noting that the requirement of Lorentzian signature implies A(r) B(r) > 0, we find two possible interpretations:

(i) The nonzero component of the source four-velocity does not have to be u⁰. This provides a connection from the above ansatz to the Kantowski–Sachs (KS) space–times.

(ii) Regions with negative A(r) and B(r) of "static" solutions in the literature must be interpreted corresponding to the tachyonic source.

The combinations of source type and four-velocity direction result in four possible cases. One is the standard case, one is identical to the KS case, and two are tachyonic. The dynamic tachyonic case was anticipated in the literature, but the static tachyonic case seems to be new. We derive Oppenheimer–Volkoff-like equations for each case, and find some simple solutions. We conclude that new "simple" black hole solutions of the above form, supported by a perfect fluid, do not exist.

Exact general solutions to the Einstein–Cartan equations are obtained for spatially flat Friedmann cosmologies with a nonminimally coupled ghost scalar field and perfect fluid. It is shown that both singular and bouncing models are possible. An analogous problem is investigated in general relativity. Some effects of torsion are elucidated. The role of perfect fluid in the Einstein–Cartan cosmology is discussed.

Isotropic quantum cosmological perfect fluid model is studied in the formalism of Rainbow gravity. It is found that the only surviving matter degree of freedom played the role of cosmic time. It is possible to find the wave packet naturally with a suitable choice of the Rainbow functions which resulted from the superposition of the wave functions of the Schrödinger–Wheeler–deWitt equation. The many-worlds interpretation of quantum mechanics is applied to investigate the behavior of the scale factor and the behavior is found to depend on the operator ordering. It is shown that the model in the Rainbow framework naturally avoids singularity and a bouncing nonsingular universe is found.

Although it ranks amongst the oldest of problems in classical general relativity, the challenge of finding new exact solutions for spherically symmetric perfect fluid spacetimes is still ongoing because of a paucity of solutions which exhibit the necessary qualitative features compatible with observational evidence. The problem amounts to solving a system of three partial differential equations in four variables, which means that any one of four geometric or dynamical quantities must be specified at the outset and the others should follow by integration. The condition of pressure isotropy yields a differential equation that may be interpreted as second-order in one of the space variables or also as first-order Ricatti type in the other space variable. This second option has been fruitful in allowing us to construct an algorithm to generate a complete solution to the Einstein field equations once a geometric variable is specified ab initio. We then demonstrate the construction of previously unreported solutions and examine these for physical plausibility as candidates to represent real matter. In particular we demand positive definiteness of pressure, density as well as a subluminal sound speed. Additionally, we require the existence of a hypersurface of vanishing pressure to identify a radius for the closed distribution of fluid. Finally, we examine the energy conditions. We exhibit models which display all of these elementary physical requirements.

Isotropic quantum cosmological perfect fluid model is studied in the formalism of Rainbow gravity. It is found that the only surviving matter degree of freedom played the role of cosmic time. With the suitable choice of the Rainbow functions it is possible to find the wave packet naturally from the superposition of the wave functions of the Schrödinger–Wheeler–deWitt equation. The many-worlds interpretation of quantum mechanics is applied to investigate the behavior of the scale factor and the behavior is found to depend on the operator ordering. It is shown that the model in the Rainbow framework may avoid singularity yielding a bouncing nonsingular universe.

We exhibit a classical lepton model based on a perfect fluid that reproduces leptonic charges and masses in arbitrarily small volumes without metric singularities or pressure discontinuities. This solution is the first of this kind to our knowledge, because to date the only classical general relativistic models that have reproduced leptonic charges and masses in arbitrarily small volumes are based on imperfect (anisotopic) fluids or perfect fluids with electric field discontinuities. We use a Maxwell–Einstein exact metric for a spherically symmetric static perfect fluid in a region in which the pressure vanishes at a boundary, beyond which the metric is of the Reissner–Nordström form. This construction models lepton mass and charge in the limit as the boundary → 0.

In this work, we studied the traversable wormholes geometry in $f(R)$ theory gravity, where $R$ is the Ricci scalar. The wormhole solutions for some assumed $f(R)$ functions are presented. The assumption of $f(R)$ is based on the fact that its behavior changed with an assumed parameter $\alpha$ rather than the deceleration parameter. Three models are presented based on the physically motivated shape function and their behaviors are studied.

We consider the synchronization of the Einstein’s flow with the Ricci-flow of the standard spatial slices of the Robertson–Walker space–time and show that associated perfect fluid solution has a quadratic equation of state and is either spherical and collapsing, or hyperbolic and expanding.

The object of the present paper is to study mixed quasi-Einstein manifolds. Some geometric properties of mixed quasi-Einstein manifolds have been studied. We also discuss $M{(\mathrm{\text{QE}})}_4$ spacetime with space-matter tensor and some properties related to it. Finally, we construct an example of a mixed quasi-Einstein spacetime.

The objective of the present paper is to study weakly Ricci symmetric spacetimes. Among others, we prove that a weakly Ricci symmetric spacetime obeying Einstein’s field equation without cosmological constant represents stiff matter. Moreover, it is shown that the local cosmological structure of a weakly Ricci symmetric perfect fluid spacetime can be identified as Petrov type $I$, $D$ or $O$. Next, we prove that a dust and dark fluid weakly Ricci symmetric spacetime satisfying Einstein’s field equation without cosmological constant is vacuum. Finally, we show the non-existence of radiation era in such a spacetime.

The Ricci tensor of a Robertson–Walker (RW) space-time is here specified by requiring constancy of the scalar curvature and a vanishing spatial curvature. By entering this Ricci tensor in Einstein’s equations (without cosmological constant), the cosmological fluid shows a transition from a pure radiation to a Lambda equation of state. In other words, the RW geometry with constant scalar curvature and flat space fixes the limit values $w=1/3$ and $w=-1$, without any hypothesis on the cosmological fluid. The value of the scalar curvature fixes the time-scale for the transition.

For this reason, we investigate the ‘toy-universe’ with Hubble parameter $h=0.673$ and temperature $T_{\mathrm{\text{CMB}}}=2.72$K. The model predicts an age of the universe in the range 7.3–13.7Gyr.

We critically analyze the models of a main-sequence star based on polytropic gases. First, we put in evidence that the hypothesis of polytropic gas is compatible with the constitutive equation of an ideal gas if the transformations inside the star are adiabatic. Then, neither the mono- or the polyphasic models of an ideal gas can be applied inside the stellar core for the existence in this region of nuclear reactions. Moreover, we prove that polyphasic models doesn’t allow the existence of C¹ solutions of the stationary hydrodynamic equations.