The effect of modified hybrid and logarithmic teleparallel gravity on the interior solutions of compact stars

The comparative analysis of dense stellar models governed by quadratic and linear equations of state

Compact anisotropic stellar distribution with linear barotropic equation of state in energy–momentum trace coupling modification of general relativity

In this paper, we investigate the charged static spherically symmetric models in [Formula: see text] theory of gravity. We consider a linear equation of state (EoS) in the background of anisotropic matter configuration. We formulate the modified field equations and implement Durgapal transformation to examine the gravitational nature of compact stellar objects. For this purpose, we choose a specific gravitational potential and electric charge intensity to analytically solve the set of field equations. We generate three special cases of solutions for specific parametric values of [Formula: see text] appearing in the expression of gravitational potential. The evolution of physical observables, such as energy density, anisotropy parameter, radial and tangential pressures and electric field intensity, are presented in all cases. Via physical analysis, it is observed that the solution of charged compact spheres satisfies acceptability criteria, models are well behaved, and depict stability and consistency in accordance with [Formula: see text] gravity for generated models.

Spherically symmetric anisotropic solutions that describe compact stellar objects within the framework of modified Rastall gravity are explored in this manuscript, where the non‐metricity scalar represented by and the trace of the energy‐momentum tensor is denoted by . To achieve this, the Karmarkar condition is applied and a relationship between the metric functions to solve the resulting field equations is established. In this framework, the field equations are constructed and the behavior of under two different scenarios is investigated. In the first scenario, a hybrid form is employed along with a linear equation of state , where and is an arbitrary constant, to derive the corresponding . In the second scenario, a logarithmic form of the coupling function is considered. The objective is to explore possible modifications to gravity by varying the parameters and in both cases, leading to hybrid, power‐law and exponential forms of gravity. The Key physical parameters such as matter variables, anisotropy, gradients, the equation of state parameter, mass function, energy conditions, and stability criteria to assess the physical acceptability of the models are explored. The observational data such as the mass and radius of the PSR J1416‐2230 pulsar are used. It is found that all the obtained solutions exhibit physically viable and stable behavior.

In this paper, we investigated new solutions for the anisotropic compact stellar model in Einstein–Gauss–Bonnet (EGB) theory. In this context, we established a set of field equations with the help of anisotropic matter configuration. The relation between pressure in the radial direction and the energy density is taken by using a linear equation of state (EoS). A well-known Boulware–Deser exterior spacetime is matched with interior spherically symmetric spacetime at the boundary of the star to determine the unknown parameters. Different physical parameters are investigated, namely, these are density, radial pressure and transversal pressure, anisotropy, mass function, compactness and surface redshift. We discussed Herrera’s cracking condition, Tolman–Oppenheimer–Volkoff (TOV), and the adiabatic index. The values of some physical quantities like density (at center and surface), compactness and surface redshift are calculated numerically for three compact stars PSR J0348+0432, PSR J0740+6620 and PSR J0030+0451. A graphical analysis of these physical quantities for a representative compact star candidate PSR J0348+0432 is also presented with various values of EGB parameter [Formula: see text]. The energy conditions for anisotropic compact star PSR J0348+0432 are satisfied, surface redshift remains within the limit and also all the stability conditions that we discussed in this work are satisfied, this validates our presented model. The effects of the GB coupling parameter [Formula: see text] on the physical parameters are depicted graphically and numerically.

General Relativistic Stars: Linear Equations of State

We study the radial oscillations of non-rotating strange stars (SSs) and their characteristic echo frequencies for three equations of state (EoS), viz., MIT Bag model EoS, linear EoS, and polytropic EoS. The frequencies of radial oscillations of these compact stars are computed for these EoSs. In total, 22 lowest radial frequencies for each of these three EoSs have been computed. First, for each EoS, we have integrated Tolman–Oppenheimer–Volkoff equations numerically to calculate the radial and pressure perturbations of SSs. Next, the mass–radius relationships for these stars are obtained using these three EoSs. Then the radial frequencies of oscillations for these EoSs are calculated. Further, the characteristic gravitational wave echo frequencies and the repetition of echo frequencies of SSs are computed for these EoSs. Our numerical results show that the radial frequencies and also echo frequencies vastly depend on the model and on the value of the model parameter. Our results also show that the radial frequencies of strange stars are maximum for polytropic EoS in comparison to MIT Bag model EoS and linear EoS. Moreover, SSs with MIT Bag model EoS and linear EoS are found to emit gravitational wave echoes. Whereas, SSs with polytropic EoS are not emitting gravitational wave echoes.

A new compact stars nonsingular model is presented with the generalized Bardeen–Hayward mass function. Generalized Bardeen–Hayward described the regular black hole, however, due to its regularity or nonsingular nature we were inspired to construct an anisotropic compact stars model. Along with the ansatz mass function, we coupled it with a linear equation of state (EoS) to find the solutions of field equations. Indeed, the new solutions are physically viable in all physical ground. The energy conditions and Tolman–Oppenheimer–Volkoff (TOV)-equation are well satisfied signifying that the mass distribution is physically possible and at equilibrium. Also, the static stability criterion, the causality condition and Abreu’s stability condition hold good and therefore configurations are physically static stable. The same condition is further supported by the condition that the adiabatic index, which is greater than the Newtonian limit, i.e. [Formula: see text]. It is also noticed that the bag constant [Formula: see text] is proportional to the surface density in our model.

This paper explores the interior configuration of various charged anisotropic compact models within the framework of f(R,T,RληTλη) gravity. The chosen model in this theory is represented by R+γRληTλη , where γ is a real-valued parameter. We adopt a static spherical metric to describe the interior of compact strange stars and derive the corresponding field equations. The solution to these equations is then obtained using the Finch-Skea metric and a linear equation of state. Taking the radius and mass of the compact star model 4U 1820-30 as a case study, we investigate the impact of charge and modified corrections on its internal distribution. The stability of the resulting model is also determined within a specific range of γ. Additionally, we determine the values of the model parameter through the vanishing radial pressure constraint, aligning with the experimental data of eight different stars. Our findings indicate that the resulting model adheres to the conditions necessary for physically relevant interiors, particularly in the case of lower charge.

Equations of state and hysteresis loops in isothermal cavitation

Charged anisotropic fluid sphere in [formula omitted] gravity satisfying Vaidya - Tikekar metric

We consider the inhomogeneous Morris–Thorne wormhole metric with matter tensors characterised by a novel linear equation of state in f(R) gravity. Using the Einstein’s field equations in metric f(R) gravity we model solutions for both wormhole as well as f(R) gravity. We obtain four different wormhole models, two wormholes are characterised by solid angle deficit, three are not asymptotically extendible, while one is asymptotically flat with zero tidal force. These are supported by four different power law f(R) models. The parameter space of the models can support both null energy conditions (NEC) satisfying as well as violating wormhole. In case of NEC satisfying matter, the associated f(R) is ghost. The f(R) models obtained have been independently substantiated for cosmological feasibility and valid parameter space was obtained corresponding to cosmologically viable f(R). Suitable scalar-tensor representation of the corresponding f(R) models have been presented using the correspondence of f(R) gravity with Brans–Dicke (BD) theory of gravity. The robustness of the wormhole solutions were further analysed with the BD scalar fields in the hybrid metric-Palatini gravity, which showed excellent results. Lastly as an independent astrophysical probe for the wormhole we have obtained the location of their photon spheres and have connected them with the Herrera Complexity factor in f(R). Our results show that the relation between the complexity factor and existence of photon spheres remains fundamentally unaltered in f(R) as compared to Einstein’s gravity.

Rastall theory propounded some five decades ago belongs to a class of modified theories of gravity. Such theories are motivated by the need to modify general relativity suitably in order to address some problems not explained by the standard theory. Amongst such issues are the observed accelerated expansion of the universe, motion in extremely high gravity regimes and explanations for the discrepancy in the value of the cosmological constant between quantum gravity and experimentation. Recently, it has been claimed that the Rastall theory is trivially equivalent to the standard Einstein theory. We investigate this claim in the context of stellar structure and elementary requirements for physical plausibility. We consider the analogue of the Saslaw et al. [Astrophys. J. 471, 571 (1996)] isothermal model of general relativity and show that the Rastall version satisfies the basic requirements unlike its counterpart. Then, we examine in turn the consequences of suppressing one of the inverse square law fall off of the energy density or the linear equation of state. Imposing a linear barotropic equation of state, we find a generalized de Sitter spacetime as an exact solution of the Rastall equations. In addition, the case of a constant spatial gravitational potential is studied. In each case, we note that the physics of the Rastall model differs from that of the Einstein version.

In this work we present a general framework for obtaining exact solutions to the Einstein field equations describing strange stars obeying a colour-flavour-locked (CFL) equation of state. Starting off with a spherically symmetric metric in isotropic coordinates describing the interior of the star, we impose a CFL equation of state to reduce the problem to a single-generating function of the gravitational potentials. Our approach leads to an infinite class of solutions of the field equations. In order to test the physical viability of our solutions, we subscribe a particular model to stringent stability tests. In particular, we show that a linear equation of state described by the MIT Bag model mimics the CFL equation of state describing strange stars with interacting quark matter. This is an interesting result which connects the more robust and mathematically tractable linear equation of state to the fundamental physics describing nuclear matter in the quark regime.

This paper aims to discuss the model of compact stars based on spherically symmetric spacetime, with a focus on the gravitational effects of Rastall teleparallel gravity, where T represents torsion and λ represents the Rastall parameter. In this study, we evaluate the spherically symmetric spacetime component e a(r) in terms of e b(r) using the linear equation of state p r = β ρ + γ, while the other component e b(r) is assumed from the literature. The paper delves into a detailed analysis of various properties of compact stars such as energy density profile, pressure components, gradients profiles, anisotropic conduct, energy limits, equation of state profiles, velocities of sound profiles, TOV equation profiles, and compactification profile. We use the well-known junction conditions to facilitate the evaluation of the unknown parameters, taking the standard Schwarzschild metric as the outer spacetime. Through detailed analysis in graphical form, we demonstrate that the model showing the anisotropic conduct of stellar objects is viably legitimate, regular, and stable. Overall, the paper provides a comprehensive analysis of the properties of compact stars, which will undoubtedly contribute to our understanding of these astrophysical phenomena.