Relativistic anisotropic stellar models with Tolman VII spacetime

We present a new class of relativistic anisotropic stellar models with spherically symmetric matter distribution in Einstein Gauss–Bonnet (EGB) gravity. A higher dimensional Finch–Skea geometry in the theory is taken up here to construct stellar models in hydrostatic equilibrium. The Gauss–Bonnet term is playing an important role in accommodating neutron stars. We study the physical features namely, the energy density, the radial and tangential pressures and the suitability of the models. It is found that the equation of state of such stars are non-linear which is determined for a given mass and radius of known stars. The stability of the stellar models are also explored for a wide range of values of the model parameters.

This study investigates anisotropic compact star configurations within the framework of [Formula: see text] gravity, employing a conformal Killing vector approach to model ultra-dense strange quark stars. Adopting the MIT bag equation of state (EOS) for strange quark matter (SQM) and a linear relation between tangential pressure and energy density, we derive exact solutions to the Einstein field equations under the modified gravity formalism. Key parameters, including the coupling constant [Formula: see text], bag constant B and anisotropy coefficient [Formula: see text], are analyzed for the representative candidate [Formula: see text]. Our results confirm the absence of geometric singularities, with metric potentials exhibiting regular behavior. Effective energy density, radial pressure and tangential pressure peak at the stellar center and decline monotonically toward the surface, while anisotropy increases radially, reaching maxima at the boundary. The model satisfies all energy conditions and adheres to the Buchdahl limit. Mass–radius relations reveal proportional increases in total mass M and radius R with rising [Formula: see text], contrasting general relativity (GR) predictions. Stability analyses via the modified Tolman–Oppenheimer–Volkoff (TOV) equation demonstrate equilibrium through force balance, with an emergent repulsive force [Formula: see text] attributed to matter-geometry coupling. Stability is further validated by Herrera’s cracking criterion and adiabatic indices. Surface redshift decreases with [Formula: see text], while compactification factors remain consistent with ultra-dense characteristics. Tabulated results highlight decreasing central density, surface density and compactness ([Formula: see text]) with increasing [Formula: see text]. This work establishes a robust, singularity-free anisotropic stellar model in [Formula: see text] gravity, offering insights into the interplay of modified gravity, anisotropy and quark matter in describing compact astrophysical objects.

We obtain a class of anisotropic spherically symmetric relativistic solutions of compact objects in hydrostatic equilibrium in the $$f(R,T) =R+2\chi T$$ modified gravity, where R is the Ricci scalar, T is the trace of the energy momentum tensor and $$\chi $$ is a dimensionless coupling parameter. The relativistic solutions are employed to obtain realistic stellar models for compact stars, and the physical quantities, energy density, anisotropy parameter, radial and tangential pressures and TOV equations are studied numerically for different model parameters. We construct anisotropic stellar models with modified Finch–Skea ansatz in the f(R, T)-theory of gravity for known mass and radius which obey all the conditions for a physically realistic star. The equation of state for the interior matter is also predicted which is of the form $$p= f(\rho )$$ . The stellar models satisfy causality conditions, and the adiabatic index is examined.

The present work is devoted to the study of anisotropic compact matter distributions within the framework of five-dimensional Einstein–Gauss–Bonnet gravity. To solve the field equations, we have considered that the inner geometry is described by Tolman–Kuchowicz spacetime. The Gauss–Bonnet Lagrangian mathcal {L}_{GB} is coupled to the Einstein–Hilbert action through a coupling constant, namely alpha . When this coupling tends to zero general relativity results are recovered. We analyze the effect of this parameter on the principal salient features of the model, such as energy density, radial and tangential pressure and anisotropy factor. These effects are contrasted with the corresponding general relativity results. Besides, we have checked the incidence on an important mechanism: equilibrium by means of a generalized Tolman–Oppenheimer–Volkoff equation and stability through relativistic adiabatic index and Abreu’s criterion. Additionally, the behavior of the subliminal sound speeds of the pressure waves in the principal directions of the configuration and the conduct of the energy-momentum tensor throughout the star are analyzed employing the causality condition and energy conditions, respectively. All these subjects are illuminated by means of physical, mathematical and graphical surveys. The M–I and the M–R graphs imply that the stiffness of the equation of state increases with alpha ; however, it is less stiff than GR.

Exploring the applicability of traversable wormhole formation in [formula omitted] gravity

In this study, we search for a new class of wormhole solutions in the framework of Brans–Dicke (BD) theory in the presence of anisotropic matter distribution. Considering a linear equation of state (EoS) between radial pressure and energy density profile we find exact static spherically symmetric solutions to the BD field equations which represent wormhole configurations. The solutions we obtain include both cases with zero and nonzero redshift functions, for which, the conditions on wormhole geometry together with the weak (WEC) and null (NEC) energy conditions put constraints on model parameters such as, the BD coupling and EoS parameters. These constraints also depend on other model parameters such as, the value of BD scalar field and energy density at the wormhole throat. The regularity of the obtained solutions is verified by calculating the Kretschmann scalar in order to ensure that curvature singularities are absent in the wormhole spacetime. We then find that BD wormholes in the presence of anisotropic matter can exist without violating NEC and WEC, either at the throat or across the entire spacetime.

In this paper, we study classical general relativistic static wormhole configurations with pseudospherical symmetry. We show that, in addition to the hyperbolic wormhole solutions discussed by Lobo and Mimoso in [Phys. Rev. D 82, 044034 (2010)], there exists another wormhole class, which is a truly pseudospherical counterpart of spherical Morris--Thorne wormhole (contrary to the Lobo--Mimoso wormhole class), since all constraints originally defined by Morris and Thorne for spherically symmetric wormholes are satisfied. We show that, for both classes of hyperbolic wormholes, the energy density, at the throat, is always negative, while the radial pressure is positive, contrary to the spherically symmetric Morris--Thorne wormhole. Specific hyperbolic wormholes are constructed and discussed by imposing different conditions for the radial and lateral pressures, or by considering restricted choices for the redshift and the shape functions. In particular, we show that a hyperbolic wormhole cannot be sustained at the throat by phantom energy and that there are pseudospherically symmetric wormholes supported by matter with isotropic pressure and characterized by space sections with an angle deficit (or excess).

We consider [Formula: see text] corrected model, i.e. [Formula: see text], where [Formula: see text] is the Ricci scalar and [Formula: see text], [Formula: see text] are arbitrary constant values, to investigate some of the interior configurations of static anisotropic spherical charged stellar structures. The existence of electric charge and a strong electric field confirms due to the higher values of pressure distribution and energy density of the matter inside the stars. Furthermore, for compact star configurations, we also consider the simplified MIT bag model equation of state (EoS) given by [Formula: see text], where [Formula: see text] is radial pressure, [Formula: see text] is energy density and [Formula: see text] is bag constant. This approach allows to find electric charge from the Einstein–Maxwell field equations. We have extensively discussed the behavior of the electric charge and anisotropic fluid distribution factor for five different values of [Formula: see text]. Interestingly, it is noticed during this study, for smaller values of [Formula: see text] we get intensity in electric charge. The Tolman–Oppenheimer–Volkoff equation (TOV), is modified in order to carry electric charge. In particular, we model the compact star candidates SAXJ 1808.4–3658 and Vela X-1 and give graphical representation of some important properties such as equilibrium condition, mass-radius ratio and surface redshift. In the end, our calculated solutions provide strong evidences for more realistic and viable charged stellar model.

An article is about mechanical effect of the physic-mechanical material properties on the radial pressure in the compression chamber during the compacting process of wood. Some general methods that describe the transformation process of axial pressure into the radial pressure are shown, As well as the mathematical or experimental methods specifying dependencies and physical conditions. Mathematical finite element method in this area is very useful, but rarely used. Common problems using FEM are the proper definition of the physical material properties in a particular stage of compaction. Material properties are greatly influenced by a number of factors such as moisture, fraction size, chemical composition, current temperature, radial macro structure, axial macrostructure, current pressure and others. The chamber material and the manufacturing processes or the state of wear has an impact on the physical conditions. In terms of tensile elastic deformations, these complex effects reflect and can be merged into several properties. The conversion of axial to radial pressure indicates that some properties of the compacted material have a major impact on the process, such as friction between material and chamber, elastic modulus and Poisson's ratio. The geometry of the pressing chamber also has a significant impact. This paper does not deal so much with the pressing chamber geometry but more so with the characteristics embodied in experimentally measurable quantities. The measurement of these properties in combination with the application of FEM methods proves to be a highly progressive method for understanding the compaction process and the engineering design of compaction machines for the production of briquettes and pellets. The article urges further examination and measurement of a wider range of material properties in the densification process.

In this paper, we present a model of a compact relativistic anisotropic star in the presence of an electric field. In order to obtain an exact solution of the Einstein–Maxwell field equations, we assume that the stellar material inside the star obeys a Chaplygin equation of state which is a nonlinear relationship between the radial pressure and the matter density. Using Tolman’s metric potential for [Formula: see text], we obtain the other metric co-efficient by employing the Karmarkar condition which is a necessary and sufficient condition for the interior spacetime of our model to be of embedding class I. Our stellar model is free from central singularity and obeys all the conditions for a realistic stellar object.

We propose a new compact stellar object model existing in a space filled with a distribution of anisotropic fluid matter for stellar configuration exposed to the hydrostatic equilibrium. An analytical solution was obtained using dark-energy (DE), which is characterized by a equation of state (EoS) of the type p=gamma rho - rho corresponding to the external Schwarzschild vacuum solution through a thin envelope. We have imposed a collective function based on an adjustable coefficient to solve the Einstein field equations (EFEs). We investigate the general physical characteristics of high-density astrophysical objects based on the required solutions, with the inside structure of the stellar objects, such as the energy conditions, stability analysis, mass function, surface redshift function, velocity of sound and compactness of stellar objects through theoretical expression as well as graphic plots. In terms of our results, the physical behavior of this model can be used to model ultra-compact objects.

Understanding the role of pressure anisotropy and dissipation is crucial for modelling compact objects’ internal structure and observable properties. In this work, we reinterpret local pressure anisotropy in relativistic stellar structures as an additional contribution to the energy density. This perspective enables the formulation of anisotropic equations of state for self-gravitating systems by incorporating anisotropy as a fundamental component. We demonstrate that this approach yields more realistic stellar models that satisfy key physical constraints, including mass-radius relationships and stability conditions. Our results are compared with observational data, particularly the inferred compactness of pulsars PSR J0740+6620 and PSR J0030+0451, showing that both anisotropic and isotropic models can describe these objects. Additionally, we examine the influence of dissipation – such as temperature gradients – on radial pressure, demonstrating that it can be modelled similarly to anisotropy. This interpretation allows the transformation of dissipative anisotropic models into equivalent non-dissipative isotropic configurations.

We present a class of relativistic solutions for compact cold stars with strange matter in a pseudo-spheroidal space-time. Considering strange matter equation of state namely, $p = \frac{1}{3}(\rho -4B)$ , where $\rho $ , $p$ and $B$ are energy density, pressure and MIT Bag parameter respectively, stellar models are obtained. In the presence of anisotropy with a pseudo-spheroidal geometry described by Vaidya-Tikekar, metric stellar models are explored where the Bag parameter varies with the energy density ( $\rho $ ) inside the compact object. We determine the density dependence of $B$ at different anisotropy. It is noted that although $B$ varies with anisotropy inside the star, finally at the surface it attains a value which is independent of the anisotropy. The Bag parameter $B$ is found to increase with an increase in anisotropy for a given compactness factor $(M/b)$ and spheroidicity $\lambda $ . It is also noted that for a star with given mass and radius, the parameter $B$ increases with the increase in $\lambda $ and finally at large $\lambda $ , it attains a constant. The equation of state (EoS) obtained here from geometrical consideration with allowed ‘B’ value is found same to that one obtains from micro-physics. The stability of the stellar models for compact stars with anisotropy in hydrostatic equilibrium obtained here is also studied.

In this paper, we amalgamate three-layer hypothesis of compact star models given by Ginzburg (Usp Fiz Nauk 103:393, 1971) with our recent works on core-envelope compact star models (Gedela et al. in Eur Phys J C 79:566, 2019; Pant et al. in Eur Phys J C 79:602, 2019) and propose a three-layered relativistic stellar model endowed with distinct equation of states (EoSs) in the realm of general relativity. Instead of considering core and envelope of a neutron star, we insert an extra layer, namely, an intermediate layer in between the core and envelope to enhance a new conceptual aspect of realistic and accurate modeling of internal structure of stellar objects. The quark core is assumed to satisfy MIT-bag EoS, an intermediate region and a thin envelope of matter are considered with modified Bose–Einstein condensate (BEC) and quadratic EoSs, respectively. Further, respective pairs of interfaces in between stellar objects are matched with Dormois–Israel conditions. We verify almost all physical and geometrical parameters, including anisotropic, radial pressure, compactification factor, energy conditions, and stability conditions using TOV equation are with viable trends and continuous with the smooth variations throughout interior of the stars.

Anisotropic charged strange stars in Krori-Barua spacetime under [formula omitted] gravity