Search

In this work, we attempt to find an anisotropic solution for a compact star generated by gravitational decoupling in f(Q)-gravity theory having a null complexity factor. To do this, we initially derive the complexity factor condition in f(Q) gravity theory using the definition given by Herrera (Phys Rev D 97:044010, 2018) and then derived a bridge equation between gravitational potentials by assuming complexity factor to be zero (Contreras and Stuchlik in Eur Phys J C 82:706, 2022). Next, we obtain two systems of equations using the complete geometric deformation (CGD) approach. The first system of equations is assumed to be an isotropic system in f(Q)-gravity whose isotropic condition is similar to GR while the second system is dependent on deformation functions. The solution of the first system is obtained by Buchdahl’s spacetime geometry while the governing equations for the second system are solved through the mimic constraint approach along with vanishing complexity condition. The novelty of our work is to generalize the perfect fluid solution into an anisotropic domain in f(Q)-gravity theory with zero complexity for the first time. We present the solution’s analysis to test its physical viability. We exhibit that the existence of pressure anisotropy due to gravitational within the self-gravitating bounded object plays a vital role to stabilize the f(Q) gravity system. In addition, we show that the constant involved in the solution controls the direction of energy flow between the perfect fluid and generic fluid matter distributions.

In this work, we employ the Karmarkar condition together with the notion of vanishing complexity (Herrera in Phys Rev D 97:044010, 2018) and isotropization technique to generate models of compact stars within the framework of complete geometric deformation. Starting off with the Kuchowicz ansatz as one of the metric potentials for the seed solution, we impose the Karmarkar condition to obtain fully the gravitational behaviour of a static compact object with anisotropic pressure. This solution is then subjected to the complete geometric deformation algorithm. The novelty in our work is to impose the condition of vanishing complexity and isotropization techniques in order to derive the deformation functions. We present two solutions of the resulting governing equations which are subjected to physical viability tests. We demonstrate that the presence of pressure anisotropy within the bounded object plays a key role in determining its stability. In addition, we show that the magnitude of the decoupling constant determines the direction of energy flow between the generic fluid and the fluid matter distribution.

We investigate the possibility of existing a class of compact charged spheres made of a charged perfect fluid in the framework of Einstein–Gauss–Bonnet theory in five-dimensional spacetime (5D EGB). In order to study spherically symmetric compact stars in EGB gravity, we prefer to apply a systematic and direct approach to decoupling gravitational sources via the minimal geometric deformation approach (MGD), which allows us to prove that the fluid must be anisotropic. In fact, we specify a well-known Krori–Barua spacetime in the MGD approach that helps us to determine the decoupling sector completely. Indeed, by using this approach, we found an exact and physically acceptable solution which satisfies all the elementary criteria of physical acceptability for a stellar solution via mimic approach. Finally, we show that the compactness factor in the presence of gravitational decoupling satisfies the Buchdahal limit under 5D EGB gravity.

In this work, we present a hierarchical solution-generating technique employing the Minimum Gravitational Decoupling (MGD) Method and the generalized concept of Complexity as applied to Class I spacetime for bounded compact objects in classical general relativity. Starting off with an anisotropic seed solution described by Class I spacetime, we apply the MGD technique with the constraint that the effective anisotropy vanishes which leads to an isotropic model. In addition, we produce a second family of solutions in which the Complexity factor [Herrera (Phys Rev D 97:044010, 2018)] for the seed solution and its MGD counterpart are the same. We discuss the physical plausibility of both classes of solutions as candidates for physically realizable compact objects.

In this article, we develop a theoretical framework to study compact stars in Einstein gravity with the Gauss–Bonnet (GB) combination of quadratic curvature terms. We mainly analyzed the dependence of the physical properties of these compact stars on the Gauss–Bonnet coupling strength. This work is motivated by the relations that appear in the framework of the minimal geometric deformation approach to gravitational decoupling (MGD-decoupling), we establish an exact anisotropic version of the interior solution in Einstein–Gauss–Bonnet gravity. In fact, we specify a particular form for gravitational potentials in the MGD approach that helps us to determine the decoupling sector completely and ensure regularity in interior space-time. The interior solutions have been (smoothly) joined with the Boulware–Deser exterior solution for 5D space-time. In particular, two different solutions have been reported which comply with the physically acceptable criteria: one is the mimic constraint for the pressure and the other approach is the mimic constraint for density. We present our solution both analytically and graphically in detail.

In the present article, we discuss relativistic anisotropic solutions of the Einstein field equation for the spherically symmetric line element under the class I condition. To do so we apply the embedding class one technique using Eisland condition. Within this approach, one arrives at a particular differential equation that links the two metric components $e^{\nu}$ and $e^{\lambda}$. In order to obtain the full space-time description inside the stellar configuration we ansatz the generalized form of metric component $g_{rr}$ corresponding to the Finch-Skea solution. Once the space-time geometry is specified we obtain the complete thermodynamic description i.e. the matter density $\rho$, the radial, and tangential pressures $p_r$ and $p_t$, respectively. Graphical analysis shows that the obtained model respects the physical and mathematical requirements that all ultra-high dense collapsed structures must obey. The $M-R$ diagram suggests that the solution yields stiffer EoS as parameter $n$ increases. The $M-I$ graph is in agreement with the concepts of Bejgar et al. \cite{bej} that the mass at $I_{max}$ is lesser by few percent (for this solution $\sim 3\%$) from $M_{max}$. This suggests that the EoSs is without any strong high-density softening due to hyperonization or phase transition to an exotic state., Comment: 14 figures, Accepted in European Physical Journal C

In this work we have extended the Maurya-Gupta isotropic fluid solution to Einstein field equations to an aniso-tropic domain. To do so, we have employed the gravitational decoupling via the minimal geometric deformation approach. The present model is representing the strange star candidate LMC X-4. A mathematical, physical and graphical analysis, shown that the obtained model fulfills all the criteria to be an admissible solution of the Einstein field equations. Specifically, we have analyzed the regularity of the metric potentials and the effective density, radial and tangential pressures within the object, causality condition, energy conditions, equilibrium via Tolman–Oppenheimer–Volkoff equation and the stability of the model by means of the adiabatic index and the square of subliminal sound speeds.

The present paper provides a new exact and analytic solution of the Einstein–Maxwell field equations describing compact anisotropic charged stars satisfying the MIT bag model equation of state for quark matter. The model is obtained by assuming the Tolman–Kuchowicz spacetime geometry (Tolman, in Phys Rev 55:364, 1939; Kuchowicz, in Acta Phys Pol 33:541, 1968). Our stellar model is free from central singularity and obeys all the conditions for a realistic stellar object. The solution is smoothly matched with the exterior Reissner–Nordstrom spacetime in order to obtain the physical parameters of the system. An interesting phenomenon which arises in this model is the fact that the force due to the pressure anisotropy initially dominates the Coulomb repulsive force, nevertheless as the radius increases the electric force dominates the anisotropic one. This may be an additional mechanism required for stability and equilibrium against the gravitational collapse of the stellar object. Detailed analyses of the obtained model are also given with the help of graphical representations.