Narrow Results

Cosmological particle production within the framework of induced gravity is investigated at the phenomenological level. It turns out that the conformal invariance of the “creation law” imposes quite strict restrictions on the possible types of sources. It is shown that terms with the particle number density in the “creation law” can be interpreted as dark matter. The action under consideration is reduced to the Einstein–Hilbert action with the classical scalar field for a certain gauge, which in turn reduces to $f(R)$-gravity with $f(R)\propto R^{\frac{3}{2}}$.

The aim of this paper is to study geometrical aspects of an almost Ricci soliton on ${(wRs)}_4$ perfect fluid spacetime obeying Einstein’s field equation. Among others, we first find the soliton constant and cosmological constant in terms of scalar curvature and potential vector field in ${(wRs)}_4$ perfect fluid spacetime. Next, we discuss some physical phenomena related to dust fluid, dark fluid, and radiation era in ${(wRs)}_4$ perfect fluid spacetime admitting an almost Ricci soliton with potential vector field as solenoidal vector field and basic vector field $\rho$ under matter collineation condition. Further, we find an inequality for soliton constant when ${(wRs)}_4$ perfect fluid spacetime obeys the timelike convergence condition. Finally, we obtain some results in a ${(wRs)}_4$ perfect fluid spacetime whose metric represents an almost Ricci soliton when basic vector field and potential vector field both are torseforming vector field $\rho$. Also, for such spacetime we find the soliton constant in terms of cosmological constant, gravitational constant, energy density, and isotropic pressure. We also provide an example of ${(wRs)}_4$ spacetime whose metric represents an almost Ricci soliton.

In this research paper, we discuss the energy–momentum-squared gravity model ${ℱ}({ℛ},{{𝒯}}^2)$ coupled with perfect fluid. We obtain the equation of state for the perfect fluid in ${ℱ}({ℛ},{{𝒯}}^2)$-gravity model. Furthermore, we deal with the energy–momentum-squared gravity model ${ℱ}({ℛ},{{𝒯}}^2)$ coupled with perfect fluid, which admits the Ricci solitons with a conformal vector field. We provide a clue in this series to determine the density and pressure in the radiation and phantom barrier periods, respectively. In addition, we investigate the different energy conditions, black holes and singularity conditions for perfect fluid attached to ${ℱ}({ℛ},{{𝒯}}^2)$-gravity in terms of Ricci soliton. Finally, we derive the Schrödinger equation for energy–momentum-squared gravity model ${ℱ}({ℛ},{{𝒯}}^2)$ coupled with perfect fluid.

In this paper, we investigate the circular motion and chaotic behavior of charged particles in the dyonic global monopole spacetime surrounded by a perfect fluid. We classified the black hole into three special regimes: dark matter, dust, and radiation. We precisely calculated the Lyapunov exponent for each regime as an eigenvalue of the Jacobian matrix. We examine, through numerical and graphical analysis, the circular motion and chaos bound violation across all the regimes. In the dark matter regime, stable orbits conform to the chaos bound. Even though the bound brings orbits with small charges and those far from the event horizon closer, they never violate it. In the dust regime, there can be more than one orbit for a fixed mass, charge, topological defect, and fluid parameter, especially when the angular momentum is small. At this point, the orbits are unstable, and those that are closer to the event horizon violate the bound. Similarly, in the radiation regime, orbits that are closer to the event horizon are unstable and chaotic, especially with greater angular momentum. In fact, regardless of the charge, topological defect, and fluid parameter, all orbits, whether they are far from or close to the horizon, become unstable and violate the bound when the angular momentum is significantly large.

We look for "static" spherically symmetric solutions of Einstein's Equations for perfect fluid source with equation of state p = wρ, for constant w. We consider all four cases compatible with the standard ansatz for the line element, discussed in previous work. For each case, we derive the equation obeyed by the mass function or its analogs. For these equations, we find all finite-polynomial solutions, including possible negative powers.

For the standard case, we find no significantly new solutions, but show that one solution is a static phantom solution, another a black hole-like solution. For the dynamic and/or tachyonic cases we find, among others, dynamic and static tachyonic solutions, a Kantowski–Sachs (KS) class phantom solution, another KS-class solution for dark energy, and a second black hole-like solution.

The black hole-like solutions feature segregated normal and tachyonic matter, consistent with the assertion of previous work. In the first black hole-like solution, tachyonic matter is inside the horizon, in the second, outside.

The static phantom solution, a limit of an old one, is surprising at first, since phantom energy is usually associated with super-exponential expansion. The KS-phantom solution stands out since its "mass function" is a ninth order polynomial.

In this paper, the effect of a positive cosmological constant on spherically symmetric collapse with perfect fluid has been investigated. The matching conditions between static exterior and non-static interior spacetimes are given in the presence of a cosmological constant. We also study the apparent horizons and their physical significance. It is concluded that the cosmological constant slows down the collapse of matter and hence limit the size of the black hole. This analysis gives the generalization of the dust case to the perfect fluid. We recover the results of the dust case for p = 0.

We investigate some exact static cylindrically symmetric solutions for a perfect fluid in the metric f(R) theory of gravity. For this purpose, three different families of solutions are explored. We evaluate energy density, pressure, Ricci scalar and functional form of f(R). It is interesting to mention here that two new exact solutions are found from the last approach, one is in particular form and the other is in the general form. The general form gives a complete description of a cylindrical star in f(R) gravity.

This paper is devoted to explore static plane symmetric solutions in metric f(R) gravity with matter as a perfect fluid. We obtain seven types of solutions. The energy density, pressure and the Ricci scalar are evaluated for each solution. Finally, we find four such solutions which satisfy the required conditions of physically acceptable solutions out of which two are singular and two nonsingular.

We impose perfect fluid concept along with slow expansion approximation to derive new solutions which, considering non-static spherically symmetric metrics, can be treated as Black Holes (BHs). We will refer to these solutions as Quasi BHs. Mathematical and physical features such as Killing vectors, singularities, and mass have been studied. Their horizons and thermodynamic properties have also been investigated. In addition, relationship with other related works (including McVittie's) are described.

We investigate cylindrically symmetric spacetimes in the context of $f(R)$ gravity. We firstly attain conformal symmetry of the cylindrically symmetric spacetime. We obtain solutions to use features of the conformal symmetry, field equations and their solutions for cylindrically symmetric spacetime filled with various cosmic matters such as vacuum state, perfect fluid, anisotropic fluid, massive scalar field and their combinations. With the vacuum state solutions, we show that source of the spacetime curvature is considered as Casimir effect. Casimir force for given spacetime is found using Wald’s axiomatic analysis. We expose that the Casimir force for Boulware, Hartle–Hawking and Unruh vacuum states could have attractive, repulsive and ineffective features. In the perfect fluid state, we show that matter form of the perfect fluid in given spacetime must only be dark energy. Also, we offer that potential of massive and massless scalar field are developed as an exact solution from the modified field equations. All solutions of field equations for vacuum case, perfect fluid and scalar field give a special $f(R)$ function convenient to $\Lambda$-CDM model. In addition to these solutions, we introduce conformal cylindrical symmetric solutions in the cases of different $f(R)$ models. Finally, geometrical and physical results of the solutions are discussed.

We analyze the impact of the inverse square law fall-off of the energy density in a charged isotropic spherically symmetric fluid. Initially, we impose a linear barotropic equation of state $p=\alpha \rho$ but this leads to an intractable differential equation. Next, we consider the neutral isothermal metric of Saslaw et al. [Phys. Rev. D13, 471 (1996)] in an electric field and the usual inverse square law of energy density and pressure results thus preserving the equation of state. Additionally, we discard a linear equation of state and endeavor to find new classes of solutions with the inverse square law fall-off of density. Certain prescribed forms of the spatial and temporal gravitational forms result in new exact solutions. An interesting result that emerges is that while isothermal fluid spheres are unbounded in the neutral case, this is not so when charge is involved. Indeed it was found that barotropic equations of state exist and hypersurfaces of vanishing pressure exist establishing a boundary in practically all models. One model was studied in depth and found to satisfy other elementary requirements for physical admissibility such as a subluminal sound speed as well as gravitational surface redshifts smaller than 2. Buchdahl [Acta Phys. Pol. B10, 673 (1965)], Böhmer and Harko [Gen. Relat. Gravit.39, 757 (2007)] and Andréasson [Commum. Math. Phys.198, 507 (2009)] mass-radius bounds were also found to be satisfied. Graphical plots utilizing constants selected from the boundary conditions established that the model displayed characteristics consistent with physically viable models.

Tilted Kantowski–Sachs cosmological model in Brans–Dicke theory for perfect fluid has been investigated. The general solution of field equations in Brans–Dicke theory for the combined scalar and tensor field are obtained by using power law relation. Also, some physical and geometrical parameters are obtained and discussed.

In this paper, we present a physically acceptable internal solution with a perfect fluid, which needs the pressure and density as regular, positive and monotonic decreasing functions and with a speed of sound positive and lower than the speed of light. This solution depends on a parameter $y$, and it is physically acceptable if $w\le 0.36068416388$, the compactness has a maximum value for the maximum value of $y$ and it corresponds to $\frac{GM}{c^{2}R}=0.1884895029$, thus the model can be applicable to the description of compact stars. In a complementary way, we present the description of a star with mass equal to the sun mass and radius of $R=7.85$ Km associated to the neutron star Her X-1, obtaining a central density ${\rho }_c=2.44986086610^{17}{\mathrm{\text{Kg/m}}}^3$ which is characteristic of the neutron stars.

The purpose of this paper is to find conformal vector fields of some perfect fluid Kantowski–Sachs and Bianchi type III spacetimes in the $f(R)$ theory of gravity using direct integration technique. In this study, there exist only eight cases. Studying each case in detail, we found that in two cases proper conformal vector fields exist while in the rest of the cases, conformal vector fields become Killing vector fields. The dimension of conformal vector fields is either 4 or 6.

We explore the problem of charged perfect fluid spherically symmetric gravitational collapse in f(R, T) gravity (R is Ricci scalar and T is the trace of energy–momentum tensor). We have taken the interior boundary of a star as spherically symmetric metric filled with the charged perfect fluid. In order to study charged perfect fluid collapse, we have investigated the exact solutions of the Maxwell–Einstein field equations solutions using the most simplified form for f(R, T) model f(R, T) = R + 2$\lambda$T, where $\lambda$ is model parameter. This study involves the effects of charge as well as coupling parameter on collapse of a star. We studied the nature of trapped surfaces, apparent horizon and singularity structure in detail. It has been found that singularity is formed earlier than the apparent horizons, so the end state of gravitational collapse in this case is black hole.

In this paper, conformal symmetric Freidmann–Robertson–Walker (FRW) universe with perfect fluid in the framework of $f(R,T)$ gravitational theory is investigated. Firstly, field equations of FRW universe with perfect fluid are obtained for $f(R,T)=R+h(T)$ modified theory of gravity. The field equations of the model have been revised to understand physical nature between matter and geometry by means of conformal symmetry in $f(R,T)$ gravitational theory. The exact solutions of conformal FRW universe with perfect fluid are attained for matter part of the $f(R,T)$ model in the case of $h(T)=\lambda T$. The $f(R,T)$ gravitational theory is one of the acceptable modifications of General Relativity (GR) in order to expound cosmic acceleration of the universe with no needing any exotic component. Nevertheless, the obtained model indicates exotic matter distribution for the current selection of arbitrary constants. Also, different value selections of arbitrary constants for the obtained model are able to predicate expanding or contracting universe with zero deceleration. Besides, it is shown that the FRW universe under the influence of the conformal Killing vector preserves to isotropic nature. Energy conditions are investigated. Also, it is shown that the constructed model satisfies strong energy condition (SEC) in all cases.

Starting from the construction of a solution for Einstein’s equations with a perfect fluid for a static spherically symmetric spacetime, we present a model for stars with a compactness rate of $u\le 0.114508$. The model is physically acceptable, that is to say, its geometry is non-singular and does not have an event horizon, pressure and speed of sound are bounded functions, positive and monotonically decreasing as function of the radial coordinate, also the speed of sound is lower than the speed of light. While it is shown that the adiabatic index $\gamma >14.615$, which guarantees the stability of the solution. In a complementary manner, numerical data are presented considering the star PSR J0737-3039A with observational mass of $1.3381M_{\odot }$, for the value of compactness $0.105395$, which implies the radius $R=18745.32\mathrm{\text{m}}$ and the range of the density ${\rho }_b=0.931561\times 10^{17}{\mathrm{\text{kg/m}}}^3$$\le \rho \le 1.012207\times 10^{17}{\mathrm{\text{kg/m}}}^3={\rho }_c$, where ${\rho }_c$ and ${\rho }_b$ are the central density and the surface density, respectively. This range is consistent with the expected values; as such, the model presented allows to describe this type of stars.

The concept of dark matter has been imported to explain the observed velocity profile of the spiral galaxies, the flat rotational velocity. Taking the flatness of rotation curves as an input and assuming that the galactic halo is filled with charged perfect fluid having known mass density function, we obtain a space time metric in the galactic halo region. The acquired solution indicates to a (nearly) flat universe, consistent with the present day cosmological observations. Various other aspects of the solution such as attractive gravity in the halo region, stability of the circular orbit, etc., are also analyzed.

In the description of neutron stars, it is very important to consider gravitational theories as general relativity, due to the determining influence on the behavior of the different types of stars, since some objects show densities even bigger than nuclear density. This paper starts with Einstein’s equations for a perfect fluid and then we present a uniparametric stellar model which allows to describe compact objects like neutron stars with compactness ratio $u\le 0.2533053$. The pressure and density are monotone decreasing regular functions, the speed of sound satisfies the causality condition, while the value for its adiabatic index $\gamma =4.9227102>4/3$ guarantees the stability. In addition, the graph of $P$ versus $\rho$ shows a quasi-linear relationship for the equation of state $P(\rho )=P_c(\rho -{\rho }_b)/({\rho }_c-{\rho }_b)$, which is similar to the so-called MIT Bag equation when we have the interaction between quarks. In our case it is due to the interaction of the different components found inside the star, such as electrons and neutrons. As an application of the model, we describe the star PSR J1614-2230 with a observed mass of $M=(1.97\pm 0.04)M_{\odot }$ and a radius $R=(13\pm 2)\mathrm{\text{km}}$, the model shows that the maximum central density occurs for a maximal compactness value ${\rho }_c=7.8065214\times 10^{17}{\mathrm{\text{kg/m}}}^3$.

In this paper, the higher-dimensional collapse of homogeneous isotropic perfect fluid is studied by considering the geometry of five-dimensional spherically symmetric metric. Using equations of state for different fields like dust, radiation and stiff fluid with and without cosmological constant $\mathrm{\Lambda }$, the gravitational collapse is studied. The results are compared with the usual four-dimensional study in [A. V. Astashenok, K. Mosani, S. D. Odintsov and G. C. Samanta, Int. J. Geom. Methods Mod. Phys. 16, 1950035 (2019)]. It is found that the collapse rate is faster in five-dimensional spacetime as compared to four-dimensional case supporting the cosmic censorship hypothesis.