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The main aim of this study is to explore the existence and salient features of spherically symmetric relativistic quark stars in the background of massive Brans-Dicke gravity. The exact solutions to the modified Einstein field equations are derived for specific forms of coupling and scalar field functions using the equation of state relating to the strange quark matter that stimulates the phenomenological MIT-Bag model as a free Fermi gas of quarks. We use a well-behaved function along with the Karmarkar condition for class-one embedding as well as junction conditions to determine the unknown metric tensors. The radii of strange compact stars viz., PSR J1416-2230, PSR J1903+327, 4U 1820-30, CenX-3, and EXO1785-248, are predicted via their observed mass for different values of the massive Brans-Dicke parameters. We explore the influences of the mass of scalar field , coupling parameter , and bag constant on state determinants and perform several tests on the viability and stability of the constructed stellar model. Conclusively, we find that our stellar system is physically viable and stable as it satisfies all the energy conditions and necessary stability criteria under the influence of a gravitational scalar field.

The present work is focused on the investigation of the existence of compact structures describing anisotropic matter distributions within the framework of modified gravity theories, specifically $f(R,\mathcal{T}$) gravity theory. Additionally, we have taken $f(R,\mathcal{T})$ as a linear function of the Ricci scalar $R$ and the trace of the energy-momentum tensor $\mathcal{T}$ as $f(R,\mathcal{T})=R+2\ensuremath{\chi}\mathcal{T}$, where $\ensuremath{\chi}$ is a dimensionless coupling parameter, and the Lagrangian matter ${\mathcal{L}}_{m}=\ensuremath{-}\frac{1}{3}(2{p}_{t}+{p}_{r})$, to describe the complete set of field equations for the anisotropic matter distribution. We follow the embedding class I procedure using the Eisland condition to obtain a full space-time description inside the stellar configuration. Once the space-time geometry is specified, we determine the complete solution of modified Einstein equations by using the MIT bag model equation of state ${p}_{r}=\frac{1}{3}(\ensuremath{\rho}\ensuremath{-}4B)$ that describes the strange quark matter (SQM) distribution inside the stellar system, where $B$ denotes a bag constant. The physical validity of our anisotropic solution is confirmed by executing several physical tests. It is worth mentioning that with the help of the observed mass values for the various strange star candidates, we have predicted the exact radii by taking different values for $\ensuremath{\chi}$ and $B$. These predicted radii show a monotonic decreasing nature as the parameter $\ensuremath{\chi}$ is moved from $\ensuremath{-}0.8$ to 0.8 progressively. In this case, our anisotropic stellar system becomes more massive and transforms into more dense compact stars. We also perform a detailed graphical analysis of the compact star. As a result, for $\ensuremath{\chi}l0$, the current modified $f(R,\mathcal{T})$ gravity seems promising to explain the observed massive compact astrophysical objects, similar to magnetars, massive pulsars, and Chandrasekhar super white dwarfs, which are not justified in the framework of general relativity. Finally, we note that when $\ensuremath{\chi}=0$, general relativity results for anisotropic matter distributions are recovered.

In the present work, we try to find a solution without singularity of Einstein’s field equations for the spherically symmetric perfect fluid objects, accurately strange quark spheres, taking into consideration Schwarzschild metric as the outside space-time. An ensemble of inside solutions found on the basis of the simplest linear state equation in the specific form $$p_r =\alpha \rho -\beta $$ . The energy density $$\rho (r)$$ , the radial pressure $$p_r (r)$$ and the tangential pressure $$p_t (r)$$ are devoid of any singularity and exhibit a well-behaved nature within the generalized anisotropic solution for compact spherical object. The generalized TOV equation is very much preserved inside the system and all energy conditions are excellent. The stability of the matter distribution of our system is checked by the concept of Herrera’s cracking and the condition of causality is all around fulfilled for our models. The adiabatic index of our specific configuration is greater than 4 / 3 in all interior points of the system and the mass-to-radius ratio in our situation is determined also lies within the Buchdahl limit i.e. $$\hbox {M}/\hbox {R}\le 4/3\,\left( {\approx 0.444} \right) $$ . We explore the physical characteristics based on the analytical model developed for relativistic compact stellar spheres inside the framework of the general theory of relativity. The evaluated mass and radius are in close concurrence with the observational information. We show that various physical characteristics of the known strange spherical object, viz. PSR J1614-2230, Vela X-1, 4U 1608-52, PSR J1903+327, 4U 1820-30, Cen X-3, Her X-1, and SAX J1808.4-3658, can be described by the current model.

The observations of pulsars heavier than 2 M ⊙ have put strong constraints on the equation of state (EoS) above nuclear saturation density. For this reason, the internal structure of a neutron star which is strictly correlated with the EoS is an active area of investigation in theoretical astrophysics. Here, we investigate the possible sequels for the quark stars consisting of a homogeneous and unpaired charge-neutral 3-flavor interacting quark matter with O ( m s 4 ) corrections that accounts for the quark strong interactions. In particular, the quark stars (QSs) with a well-motivated quantum chromodynamics (QCD) EoS are presented in Einstein gravity with the Gauss–Bonnet (GB) combination of quadratic curvature terms. We analyze the dependence of the physical properties of these QSs on the Gauss–Bonnet coupling strength. In fact, the existence and stability of QSs depend on the effects of fourth-order corrections parameter ( a 4 ) of the QCD perturbation. We also present and discuss the calculated results for mass–central mass density ( M – ρ c ) relation and also the mass–radius (M–R) relation of QSs. Nevertheless, such deviations may be observable in future astrophysical probes.

The present paper is devoted to investigating the possibility of getting stellar interiors for ultra-dense compact spherical systems portraying an anisotropic matter distribution, employing the gravitational decoupling by means of Minimal Geometric Deformation (MGD) procedure within the modified theory of gravity: f ( R , T ) . In this regard, we have considered the algebraic function as f ( R , T ) = R + 2 χ T . The corresponding effective stress–energy tensor is conserved as well as the exact solutions are derived, where χ indicates a coupling constant which incorporates a new gravity aspect in the system. However, the MGD was introduced through a coupling constant α which makes the fluid go beyond to the perfect fluid–structure (i.e. introduce anisotropy). In this connection, we also discussed how both parameters α and χ affect the system. Moreover, the physical quantities associated with the new solutions are well-behaved from the physical and mathematical point of view which are affirmed by performing several physical tests of the main salient features, such pressure, density, dynamical equilibrium, energy conditions, and dynamical stability. We also performed the junction conditions for this chosen linear f ( R , T ) function. On the other hand, we have generated the M − R curves from our solutions in different scenarios, including GR, GR+MGD, f ( R , T ) and f ( R , T ) + MGD, and we found a perfect fit for many compact spherical objects in these scenarios by varying α and χ . The present study reveals that the modified f ( R , T ) gravity through gravitational decoupling by means of MGD method is a suitable theory to explain compact stellar structures.

We have explored exact solutions free from any physical and geometrical singularities, as well as the existence of compact stellar systems throughout linear and Starobinsky- f ( R , T ) − gravity theory. As we generally well-known, the general exact solutions of the altered Einstein Field Equations (EFEs) in the background of this gravity theory are one of the most complex tasks. To acquire simpler solution of the altered field equations, we consider linear and Starobinsky shape of the algebraic function as f ( R , T ) = R + 2 χ T and f ( R , T ) = R + ξ R 2 + 2 χ T (where R is scalar curvature, T is the trace of the stress–energy tensor and χ & ξ denotes a coupling constants). In this regards, we propose metric potentials e λ , and obtain the other metric potentials ( e ν ) under the embedding class one condition. We then compare the cases when ξ = χ = 0 [GR], ξ = 0 , χ = 0 . 5 [ f L ( R , T ) ], ξ = 0 . 5 , χ = 0 [ f S ( R , T ) ] and ξ = χ = 0 . 5 [ f S + L ( R , T ) ]. The obtained solution is well-behaved in all physical and mathematical points of view. Further, we provided a detailed physical acceptability of the solution by exploring main salient characteristics under different physical analysis in the linear f ( R , T ) − gravity. Moreover, the generalizing M − R and M − I curves from our solution are well fitted with observational data of the three compact objects viz., PSR J1614-2230, Vela X-1 and 4U 1820-30. We also found the beautiful results that the equation of state (EoS) is stiffest in χ = 0 than χ ≠ 0 , and the sensitivity in EoS is better in I − M graph than in M − R graph. Finally, we have successfully represented the effects of all the physical requirements in the arena of f ( R , T ) − gravity and we compared them with the standard GR results which can be recovered at χ = 0 .

The understanding of dark matter objects is one of the modern mysteries. Usually one interprets them as black holes, but there is no empirical evidence only a lack of alternatives. Proposing the idea of a phantom gravastar we will give an alternative explanation to these dark matter objects without supposing them to be black holes, in particular to the SgrA* and the MACHOs.

In this paper, we investigate gravastar configurations in which the interior of the compact object is modeled through a Chaplygin fluid. This is motivated by the fact that Chaplygin fluid and the associated exotic equation of state, have often been used as models for the dark energy sector. We derive the relativistic equations of the stellar structure for non-rotating configurations. A special focus is denoted in particular to the mass-radius function and the equation of state for the shell of the gravastars, for which we derive the analytical expressions.

We provide a general framework of global behavior of static solutions of spherically symmetric objects for the modeling of compact objects, making it an ideal fluid to study, analytically and numerically. We demonstrate that every single conceivable solution can be acquired by means of a solitary creating function characterized as far as one of the gravitational possibilities. We demonstrate that our answers can be used to display specific object applicants, for example, RX J 186-37, Her X-1, SAX J11808.4-3658 (SS1), SAX J11808.4-3658 (SS2) and PSR J1614-2230.