Narrow Results

The objective of this paper is to deal with physical features of charged anisotropic compact objects in the framework of $f(R,\varphi ,X)$ modified theory of gravity. To accomplish the desired objective, we consider a spherically symmetric spacetime with charged anisotropic fluid distribution. In addition, we utilize the Krori–Barua metric, i.e. $\lambda (r)=X{r}^2+Y$ and $\beta (r)=Z{r}^2$ for exploring the field equations. Moreover, we compare the interior boundary to the bardeen model as an exterior geometry to calculate the unknown constrains. Further, to check the existence of bardeen stellar structure, we discuss the behavior of physical properties such as energy density, pressure components, anisotropy, equation of state parameters, stability analysis, energy bounds, equilibrium condition, adiabatic index, compactness factor and surface redshift. Conclusively, all the obtained results show that the system under consideration is physically stable, free from singularity and viable.

The exact solutions of the Einstein field equations for dark energy in Kaluza–Klein metric under the assumption on the anisotropy of the fluid are obtained by applying the law of variation of Hubble parameter which yields the constant value of deceleration parameter. The isotropy of the fluid, space and expansion are examined.

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.

This paper studies the effects of charge on spherically symmetric collapse of anisotropic fluid with a positive cosmological constant. It is observed that electromagnetic field places restriction on the bounds of cosmological constant, which acts as repulsive force against the contraction of matter content and hence the rate of destruction is faster in the presence of electromagnetic field. We have also noted that the presence of charge affects the time interval between the formation of cosmological horizon (CH) and black hole horizon (BHH). When the electric field strength E(t, r) vanishes, our investigations are in full agreement with the results obtained by Ahmad and Malik [Int. J. Theor. Phys.55, 600 (2016)].

In this paper, the spherically symmetric gravitational collapse of anisotropic fluid in the presence of charge in metric $f(R)$ theory is analyzed. We consider the static and non static spherically symmetric spacetimes for outer and inner regions of collapsing object respectively. For the smooth matching of inner and outer regions, the Senovilla as well as Darmois matching conditions are utilized. The closed form solutions are obtained from field equations. Moreover, we examine the apparent horizons and their physical significance. The effect of cosmological constant and $f(R)$ term is same and the collapsing rate speeds up as compared to that of anisotropic fluid case when the electromagnetic field is introduced. Electromagnetic charge also affects the time interval of singularities and cosmological horizons.

We develop a new model for a spherically symmetric dark matter fluid sphere containing two regions: (i) Isotropic inner region with constant density and (ii) Anisotropic outer region. We solve the system of field equation by assuming a particular density profile along with a linear equation of state. The obtained solutions are well-behaved and physically acceptable which represent equilibrium and stable matter configuration by satisfying the Tolman–Oppenheimer–Volkoff (TOV) equation and causality condition, condition on adiabatic index, Harrison–Zeldovich–Novikov criterion, respectively. We consider the compact star EXO 1785-248 (Mass $M=1.3M_{\odot }$ and radius R$=$8.8 km) to analyze our solutions by graphical demonstrations.

A class of solutions of Einstein field equations satisfying Karmarkar embedding condition is presented which could describe static, spherical fluid configurations, and could serve as models for compact stars. The fluid under consideration has unequal principal stresses i.e. fluid is locally anisotropic. A certain physically motivated geometry of metric potential has been chosen and codependency of the metric potentials outlines the formation of the model. The exterior spacetime is assumed as described by the exterior Schwarzschild solution. The smooth matching of the interior to the exterior Schwarzschild spacetime metric across the boundary and the condition that radial pressure is zero across the boundary lead us to determine the model parameters. Physical requirements and stability analysis of the model demanded for a physically realistic star are satisfied. The developed model has been investigated graphically by exploring data from some of the known compact objects. The mass-radius (M-R) relationship that shows the maximum mass admissible for observed pulsars for a given surface density has also been investigated. Moreover, the physical profile of the moment of inertia (I) thus obtained from the solutions is confirmed by the Bejger–Haensel concept.

A static anisotropic relativistic fluid sphere model with regular geometry and finite hydrostatic functions is presented. In the interior of the sphere, the density, radial pressure and tangential pressure are positives, monotonically decreasing with increasing radius and the radial pressure vanishes at the surface of the matter distribution and is joined continuously to the exterior Schwarzschild’s solution at this surface. The speeds of the radial and tangential sound are positive and lower than the speed of light, that is, the causal condition is not violated, and also the behavior of these guarantees that the model is potentially stable. Furthermore, the range of the compactness ratio is characteristic of compact stars and it is shown that the effect of the anisotropy generates that the speed of the radial sound can behave as a function monotonically increasing or monotonically decreasing.

A stellar model with an electrically charged anisotropic fluid as a source of matter is presented. The radial pressure is described by a Chaplygin state equation, $P_r(\rho )=\mu c^2\rho -\nu /(c^2\rho )$, while the anisotropy $\mathrm{\Delta }\equiv P_t-P_r=r^{2}f(r)$ is annulled in the center of the star $(f(r)$ is regular and $f(0)\ne 0)$, the electric field, is also annulled in the center. The density pressures and the tangential speed of sound are regular, while the radial speed of sound is monotonically increasing. The model is physically acceptable and meets the stability criteria of Harrison–Zeldovich–Novikov and in respect of the cracking concept the solution is unstable in the region of the center and potentially stable near the surface. A graphic description is presented for the case of an object with a compactness rate $u=0.27336$, mass $M=1.77M_{\odot }$ and radius $R=9.56$ km that matches the star Vela X-1. Also, the interval of the central density ${\rho }_c\in [1.176977292,1.308791129]10^{18}\mathrm{\text{kg}}/{\mathrm{\text{m}}}^3$, which is consistent with the expected magnitudes for this type of stars, which shows that the behavior is accurate for describing compact objects.

In this work, the analysis of the behavior of an interior solution in the frame of Einstein’s general theory of relativity is reported. Given the possibility that, for greater densities than the nuclear density, the matter presents anisotropies in the pressures and that these are the orders of density present in the interior of the compact stars, the solution that is discussed considers that the interior region contains an anisotropic fluid, i.e. $P_r\ne P_t$. The compactness value, where $u=\frac{GM}{c^{2}R}$, for which the solution is physically acceptable is $u\le 0.23577$ as such the graphic analysis of the model is developed for the case in which the mass $M=(0.85\pm 0.15)M_{\odot }$ and the radius $R=8.1\pm 0.41\mathrm{\text{km}}$ which corresponds to the star Her X-1, with maximum compactness $u_{max}=0.1919$, although for other values of compactness $u\le 0.23577$ the behavior is similar. The functions of density and pressures are positive, finite and monotonically decreasing, also the solution is stable according to the cracking criteria and the range of values is consistent with what is expected for these type of stars.

In this paper, we investigate how the electromagnetic field influences the idea of complexity within the framework of squared gravity. The physical traits, including heat dissipation, charge, anisotropic pressure, energy density variations and correction components are found to be significant contributors of complexity in celestial objects. By employing Herrera’s orthogonal splitting approach, scalar functions are obtained yielding a complexity factor that incorporates the crucial attributes of the self-gravitating system. Furthermore, we examine the dynamics of charged spherical configuration by considering homologous mode as the simplest evolutionary pattern. Our investigation includes complexity-free scenarios (dissipative/non-dissipative) with homologous constraints. Moreover, we explore the components that contribute toward complexity during the evolutionary process. We conclude that self-gravitating structures get more complex with the inclusion of extra curvature terms of squared gravity and charge.

A spacetime endowed with an anisotropic fluid is proposed for the interior of a black hole. The geometry has an instantaneous Minkowski form and is a solution of Einstein's equations with a stress tensor on the r.h.s. obeying all the energy conditions. The interior fluid is compressible, with time dependent shear and bulk viscosity coefficients. The energy density ρ and the "radial" pressure p are proportional to 1/t², with no pressures on θ- and ϕ- directions. The model leads to a time dependent cosmological constant.

In the context of modified $f({𝒢})=\alpha {{𝒢}}^n+\beta {𝒢}ln({𝒢})$ gravity model, the current study highlights the effect of electric charge for static spherically symmetric stellar models in presence of anisotropic matter distribution. For this purpose, we specifically consider the metric potentials of Tolman–Kuchowicz space–time, which are singularity free and satisfy the stability criteria. The possible existence of charge and a strong electric field, inside the stars is due to the higher values of energy density of matter, pressure distribution and gravitational fields. For the solution of Einstein–Maxwell field equations, the simplified phenomenological MIT bag equation of state, i.e. $p_r=\frac{1}{3}(\rho -4Bg)$ and a specific form of electrical charge distribution $q(r)=Q{\left(\frac{r}{R}\right)}^3=\mathrm{\Psi }{r}^3$ are to be considered. Further, to derive the values of unknown parameters of the stellar objects, we match interior Tolman–Kuchowicz space–time to exterior Reissner–Nordström metric, at the surface of stellar system. In addition to this, for the physical validity and stability of our suggested model, we conduct several physical tests such as effective energy density, effective pressures, energy conditions, stability against equilibrium of the forces, mass-radius relation, surface redshift, Herrera’s cracking concept and electric charge for well-known compact stellar objects viz., SAX J 1808.4-3658 and PSR 1937+21. It is observed that all these tests follow the physically accepted pattern and the influence of charge leads to more stable and viable stellar structures of compact objects in $f({𝒢})$ gravity.

The dynamics of dissipative gravitational collapse of a source is explored in Rastall gravity. The field equations are derived for the geometry and collapsing matter. The dynamical equations are formulated for the heat flux and diffusion approximation. The heat transportation equation is derived by using Müller–Israel–Stewart approach to investigate the effects of heat flux on the collapsing source. Moreover, an equation is found by combining the dynamical and heat transport equation, the consequences of this equation are discussed in detail. Furthermore, the Rastall parameter $\lambda$ effect is analyzed for the collapse of sphere.

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.

A new interior solution of Einstein’s equations is derived for a static and spherically symmetric space–time that contains fluid with anisotropic pressures, characterized by a parameter N. The model presented is a generalization to a proposal which contemplated a perfect fluid, which allows us to do an analysis of the impact of the anisotropy on the compactness, density and speed of sound. Taking the observational data of the mass $M=1.7M_{\odot }$ and radius $R=9$ km as well as the mass $M=1.4M_{\odot }$ and radius $R=11$km reported for the star EXO 1745-248, it is determined that the range of values of the density varies between $5.7651\times 10^{17}$ and $1.0937\times 10^{18}$ and these increase as the anisotropy parameter increases; it also shows an effect of the anisotropy on the speed of sound. The stability of the solution is shown through the Zeldovich criteria and through the adiabatic index, and from a graphic analysis it is verified that the behavior of the density, pressures and speed of sound are physically acceptable.

We study spacetimes of spherically symmetric anisotropic fluid with homothetic self-similarity. We find a class of solutions to the Einstein field equations by assuming that the tangential pressure of the fluid is proportional to its radial one and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of these solutions are studied and found that some of them represent gravitational collapse of an anisotropic fluid.

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).

We study the evolution of an N-dimensional anisotropic fluid with kinematic self-similarity of the second kind and find a class of solutions to the Einstein field equations by assuming an equation of state where the radial pressure of the fluid is proportional to its energy density (p_r = ωρ) and that the fluid moves along timelike geodesics. As in the four-dimensional case, the self-similarity requires ω = -1. The energy conditions and geometrical and physical properties of the solutions are studied. We find that, depending on the self-similar parameter α, they may represent black holes or naked singularities. We also study the presence of dark energy in some models, and find that their existence gives rise to some constraints on the dimensions of the space–times.

We study the evolution of an anisotropic shear-free fluid with heat flux and kinematic self-similarity of the second kind. We found a class of solution to the Einstein field equations by assuming that the part of the tangential pressure which is explicitly time-dependent of the fluid is zero and that the fluid moves along timelike geodesics. The energy conditions, geometrical and physical properties of the solutions are studied. The energy conditions are all satisfied at the beginning of the collapse but when the system approaches the singularity the energy conditions are violated, allowing for the appearance of an attractive phantom energy. We have found that, depending on the self-similar parameter α and the geometrical radius, they may represent a naked singularity. We speculate that the apparent horizon disappears due to the emergence of exotic energy at the end of the collapse, or due to the characteristics of null acceleration systems as shown by recent work.