Tolman-Oppenheimer-Volkoff Equations Research Articles

Nuclear symmetry energy effects on neutron stars properties

We construct a class of nuclear equations of state based on a schematic potential model, that originates from the work of Prakash et. al. [1], which reproduce the results of most microscopic calculations. The equations of state are used as input for solving the Tolman- Oppenheimer-Volkov equations for corresponding neutron stars. The potential part contribution of the symmetry energy to the total energy is parameterized in a generalized form both for low and high values of the baryon density. The obtained nuclear equations of state are applied for the systematic study of the global properties of a neutron star (masses, radii and composition). We also address on the problem of the existence of correlation between the pressure near the saturation density and the radius.

Quintessence compact stars with Vaidya–Tikekar type grr for anisotropic fluid

The present study provides a new solution to the Einstein field equations for anisotropic matter configuration in static and spherically symmetric space–time. By taking benefit from the conformal Killing vector (CKV) technique and quintessence field specified by a parameter ωq as –1 < ωq < –1/3, we generate an exact solution to the field equations. For this investigation, we have used a specific form of metric potential taken fromVaidya–Tikekar (J. Astrophys. Astron. 3, 325 (1982)) geometry. To canvass the physical plausibility of the presented solution, we explored some analytical expressions such as energy conditions, the TOV equation, stability analysis, and equation of state parameters. We present graphical analysis of the necessary analytical expressions that revealed that our solution satisfies the necessary physical conditions.

Comment on: “Neutron star under homotopy perturbation method” Ann. Phys. 409 (2019) 167918

In this comment we discuss the application of homotopy perturbation method to a nonlinear differential mass equation that solves the Tolman–Oppenheimer–Volkoff equation for an isotropic and spherically symmetric system. We show that one obtains the same results, more easily and straightforwardly, by means of a textbook power-series method.

Gödel-type universe in f(R,G) gravity

In the current study, we discuss Gödel-type universe in [Formula: see text] gravity. Analysis has been done by considering anisotropic and perfect fluid distributions. Energy conditions for two proposed [Formula: see text] gravity models have been studied for suitable values of model parameters. Furthermore, Tolman–Oppenheimer–Volkoff equation has been developed with cylindrical coordinates in [Formula: see text] gravity. The graphical analysis for both these models suggests that Tolman–Oppenheimer–Volkoff equation is obeyed in a specific interval for the radial coordinate [Formula: see text]. A polytropic equation of state has been discussed for two [Formula: see text] gravity models. By analyzing the energy conditions, it is concluded that Gödel-type universe with both [Formula: see text] gravity models supports the expansion of the universe for certain range of radial coordinates.

Static spherically symmetric Einstein-æther models II: Integrability and the modified Tolman–Oppenheimer–Volkoff approach

We investigate the existence of analytic solutions for the field equations in the Einstein-æther theory for a static spherically symmetric spacetime and provide a detailed dynamical systems analysis of the field equations. In particular, we investigate if the gravitational field equations in the Einstein-æther model in the static spherically symmetric spacetime possesses the Painlevè property, so that an analytic explicit integration can be performed. We find that analytic solutions can be presented in terms of Laurent expansions only when the matter source consists of a perfect fluid with a linear equation of state (EoS) μ=μ0+h−1p,h>1. In order to study the field equations we apply the Tolman–Oppenheimer–Volkoff (TOV) approach and other approaches. We find that the relativistic TOV equations are drastically modified in Einstein-æther theory, and we explore the physical implications of this modification. We study perfect fluid models with a scalar field with an exponential potential. We discuss all of the equilibrium points and discuss their physical properties.

The properties of neutron star in the framework of relativistic Hartree–Fock model with unitary correlation operator method

The properties of neutron star are studied in the framework of relativistic Hartree–Fock (RHF) model with realistic nucleon–nucleon (NN) interactions, i.e., Bonn potentials. The strong repulsion of NN interaction at short range is properly removed by the unitary correlation operator method (UCOM). Meanwhile, the tensor correlation is neglected due to the very rich neutron environment in neutron star, where the total isospin of two nucleons can be approximately regarded as [Formula: see text]. The equations of state of neutron star matter are calculated in [Formula: see text] equilibrium and charge neutrality conditions. The properties of neutron star, such as mass, radius and tidal deformability, are obtained by solving the Tolman–Oppenheimer–Volkoff equation and tidal equation. The maximum masses of neutron from Bonn A, B, C potentials are around [Formula: see text]. The radius are [Formula: see text][Formula: see text]km at [Formula: see text], respectively. The corresponding tidal deformabilities are [Formula: see text]. All of these properties are satisfied with the recent observables from the astronomical and gravitational wave devices and are consistent with the results from the relativistic Brueckner–Hartree–Fock model.

Stability analysis of neutron stars in Palatini f(R, T) gravity

In this paper, we have studied the stability of neutron stars in the background of Palatini f(R, T) gravity. In this context, the static spherically symmetric geometry is considered which is assumed to be coupled with an isotropic matter configurations. The evolution of the system is considered with the help of Tolman–Oppenheimer–Volkoff equations and conformal transformations. We found the stable configurations of the spherical stars with some constraints.

Ultra‐compact objects in semiclassical gravity

AbstractIn this investigation, we study the structure of ultra‐compact stars in the framework of semiclassical gravity, an extension of Einstein's general relativity (GR), in which a classical spacetime metric is coupled to the quantum expectation value of the stress tensor and that incorporates the polarization of the quantum vacuum in the presence of a gravitational field. In this approach, a generalization of the classical Tolman–Oppenheimer–Volkoff (TOV) equations may be derived. Unlike most theoretical treatments based on GR, this formulation allows a wider range of consistent equation of state (EoS) solutions with enough compactness to produce a photon sphere without violating the Buchdahl limit, an upper bound on the compactness, thus motivating future studies to investigate if ultra‐compact stars could act as black hole mimickers. The main novelty of this extended formalism, when compared to the conventional form of the TOV equations, is the presence of an additional repulsive term—due to quantum corrections originated by the phenomenon of quantum vacuum polarization—that can withstand, under certain conditions, the gravitational collapse. Although the quantum corrections furnished by semiclassical gravity are negligible in most compact stars scenarios, for ultra‐compact configurations, where the star radius is not much larger than its gravitational radius, such effects may be relevant.

The “Planckonions”

We consider a spherically symmetric stellar configuration with a density profile [Formula: see text]. This configuration satisfies the Schwarzchild black hole condition [Formula: see text] for every [Formula: see text]. We refer to it as “Planckonion”. The interesting thing about the Planckonion is that it has an onion-like structure. The central sphere with radius of the Planck-length [Formula: see text] has one unit of the Planck-mass [Formula: see text]. Subsequent spherical shells of radial width [Formula: see text] contain exactly one unit of [Formula: see text]. We study this stellar configuration using Tolman–Oppenheimer–Volkoff equation and show that the equation is satisfied if pressure [Formula: see text]. On the geometrical side, the space component of the metric blows up at every point. The time component of the metric is zero inside the star but only in the sense of a distribution (generalized function). The Planckonions mimic some features of black holes but avoid appearance of central singularity because of the violation of null energy conditions.

Stable wormhole existence under noncommutative distributed background in Rastall theory

This study describes the Rastall modified theory with noncommutative Gaussian- and Lorentzian-like distributions to find spherical and symmetric wormhole solutions. The basic concept of noncommutative geometry with both distributions is a physically acceptable and significant topic of quantum physics. It becomes more illustrious and interesting when we combine it with the concept of wormhole geometry. Therefore, it calculates the viable and physically realistic solutions for wormhole existential geometry under Gaussian and Lorentzian frameworks. Further, in the presence of Gaussian and Lorentzian distributions, the feasible and acceptable wormhole solutions are shown graphically. Furthermore, the stability analysis is discussed by using the Tolman–Oppenheimer–Volkov equation for all of the solutions under Gaussian- and Lorentzian-like distributions in the Rastall framework. For this purpose, we will take suitable particular values of the free and dimensionless parameters. At the end, it is concluded that our obtained solutions are physically arguable.

Stability of charged neutron star in Palatini f(R) gravity

In this work, we discuss the stability of charged neutron star in the background of [Formula: see text] gravity and construct the generalized Tolman–Oppenheimer–Volkoff (TOV) equations. For this, we consider static spherically symmetric geometry to construct the hydrostatic equilibrium equation and deduce TOV equations from modified field equations with electromagnetic effects. We conclude that the generalized TOV equation depicts the stable stars configuration independent of the generic function of the modified gravity if the condition of uniform entropy and chemical composition is assumed.

Minimally deformed anisotropic model of class one space-time by gravitational decoupling

In this article, we have presented a static anisotropic solution of stellar compact objects for self-gravitating system by using minimal geometric deformation techniques in the framework of embedding class one space-time. For solving of this coupling system, we deform this system into two separate system through the geometric deformation of radial components for the source function lambda (r) by mapping: e^{-lambda (r)}rightarrow e^{-tilde{lambda }(r)}+beta ,g(r), where g(r) is deformation function. The first system corresponds to Einstein’s system which is solved by taking a particular generalized form for source function tilde{lambda }(r) while another system is solved by choosing well-behaved deformation function g(r). To test the physical viability of this solution, we find complete thermodynamical observable as pressure, density, velocity, and equilibrium condition via. TOV equation etc. In addition to the above, we have also obtained the moment of inertia (I), Kepler frequency (v), compression modulus (K_e) and stability for this coupling system. The M–R curve has been presented for obtaining the maximum mass and corresponding radius of the compact objects.

Viable wormhole solutions through Noether symmetry in [formula omitted] gravity

This paper explores static wormhole solutions through Noether symmetry technique in the framework of f(G,T) gravity, where G and T indicate the Gauss–Bonnet invariant and trace of the energy-momentum tensor, respectively. We consider isotropic fluid configuration to derive the symmetry generators with conserved parameters. We evaluate possible viable wormhole solutions and explore their stable behavior by considering the Tolman–Oppenheimer–Volkoff equation. For different forms of the red-shift parameter, we examine the effects of curvature-matter coupling as well as shape function on wormhole geometry. The graphical behavior of null/weak energy bounds for ordinary as well as effective energy-momentum tensor is investigated. We conclude that viable wormhole solutions exist for a specific functional form of this gravity.

Existence and classification of pseudo-asymptotic solutions for Tolman–Oppenheimer–Volkoff systems

The Tolman–Oppenheimer–Volkoff (TOV) equations are a partially uncoupled system of nonlinear and non-autonomous ordinary differential equations which describe the structure of isotropic spherically symmetric static fluids. Nonlinearity makes finding explicit solutions of TOV systems very difficult and such solutions are very rare. In this paper we introduce the notion of pseudo-asymptotic TOV systems and we show that the space of such systems is at least fifteen-dimensional. We also show that if the system is defined in a suitable domain (meaning the extended real line), then well-behaved pseudo-asymptotic TOV systems are genuine TOV systems in that domain, ensuring the existence of new fourteen analytic solutions for extended TOV equations. The pseudo-asymptotic solutions are classified according to the nature of the matter (ordinary or exotic) and to the existence of cavities and singularities. It is shown that at least three of them are realistic, in the sense that they are formed only by ordinary matter and contain no cavities or singularities.

Deformation of neutron stars due to poloidal magnetic fields

Abstract The mass–radius (MR) relation of deformed neutron stars in the axially symmetric poloidal magnetic field is calculated. The MR relation is obtained by solving the Hartle equations, whereas the one for spherical stars is obtained by the Tolman–Oppenheimer–Volkoff equations. The anisotropic effects of the poloidal magnetic fields are found to be non-negligible for a strong magnetic field more than $3\times10^{18}$ G at the center of a neutron star.

Possible maximum mass of dark matter existing in compact stars based on the self-interacting fermionic model

The dark matter admixed neutron stars (DANSs) are studied using the two-fluid TOV equations separately, in which the normal matter (NM) and dark matter (DM) are simulated by the relativistic mean field theory and self-interacting fermionic model, respectively. A universal relationship [Formula: see text] is suggested, where [Formula: see text] is the maximum mass of DM existing in DANSs, [Formula: see text] is the particle mass of DM ranging from 5[Formula: see text]GeV to 1[Formula: see text]TeV, [Formula: see text] is the interaction mass scale with the value 300[Formula: see text]GeV (0.1[Formula: see text]GeV) for weak (strong) interaction DM model. This simple formula connects directly the microcosmic nature of DM particle with its macrocosmic mass existing in DANSs. Meanwhile, such a formula exhibits that the existence of NM has little effect on [Formula: see text]. It is found that the ratio of radius of DM in DANSs over [Formula: see text] is a constant with the value about 12[Formula: see text] (7[Formula: see text]) for weak (strong) interaction DM cases. According to the calculated results, only for the strong interaction DM cases with [Formula: see text] to [Formula: see text][Formula: see text]GeV and central energy density [Formula: see text][Formula: see text]MeV/fm3, DM has obvious effect on the mass of compact star. Compared with the energy density of DM in the Milky Way galaxy, [Formula: see text][Formula: see text]MeV/fm3, the existence of DM might hardly affect the mass of compact stars in the Milky Way galaxy.

Applications Of The Extended Tolman-Oppenheimer-Volkoff Equation In f (R)Gravity

The Tolman-Oppenheimer-Volkoff (TOV) equation determines the structure of a spherically symmetric body of isotropic material in equilibrium, in general relativity (GR). It is widely used in the study of properties of compact stars. In case of charged compact stars, an extended TOV equation was found first by Bekenstein in 1971.We aim to use, the f (R ) theory of gravity, one among several proposed extended theories of gravity to find an equivalent equation to TOV equation, and use it to study electrically charged compact stars. We assume that the charge density is proportional to the energy density of the star and we choose the polytropic equation of state to describe the state of the charged star. We perform a detailed numerical study using Maple 2016, and our results are compared to those found in the literature in the framework of GR.

The Structure of Cold Neutron Star With a Quark Core Within the MIT and NJL Models

Neutron star due to their high interior matter density are expected to be composed of a quark core, a mixed quark-hadron matter, and a layer of hadronic matter. Thus, in this paper, we compute the equation of state of these parts of neutron star to evaluate its structure properties. We use two models for describing EOS of quark matter, NJL and MIT bag models, and employ three approaches in this work. A density dependent bag constant satisfy the quark confinement in the simple MIT bag model. We also study the interaction behavior of quarks, firstly one gluon exchange within MIT bag model and the secondly dynamical mass will be held as effective interaction that roles between particles. Density dependence of quark mass is obtained from NJL self consistent model. NJL model is a effective manner for justify the chiral symmetry. Applying the Gibbs conditions the equation of state of the quarks and hadrons mixed phase is obtained. Since the hadronic matter is under the influence of strong force of nucleons, we calculate the equation of state of this phase using a powerful variational many-body technique. Finally, we calculate the mass and radius of a cold neutron star with a quark core by numerically solving the TOV equation. To check our used EOS, we compare our results with the recent observational data. Our results are in a good agreement with some observed compact objects such as $SAXJ1748.9-2021$, $4U1608-52$ and $Vela X-1$.

Compact Stars with Modified Gauss–Bonnet Tolman–Oppenheimer–Volkoff Equation

We study compact stars for f( $$\mathcal{G}$$ ) gravity model using modified Tolman–Oppenheimer–Volkoff equation. Firstly, the hydrostatic equilibrium equations have been developed in the context of f( $$\mathcal{G}$$ ) gravity. Secondly, the profiles of energy density, pressure and mass of stars are investigated through two different equations of state models, p = ωρ5/3 and p = a(ρ – 4b), ρ being the energy density, ω, a and b are the specific constants. For f( $$\mathcal{G}$$ ) = α $${{\mathcal{G}}^{2}}$$ model with α being an arbitrary constant, the physical attributes of the compact objects have been discussed for the different values of model parameter α. It is concluded that in the framework of f( $$\mathcal{G}$$ ) gravity, neutron and strange stars follow physically accepted patterns and the results agree with those already available in literature.

Compact star models in class I spacetime

In the present article, we have presented completely new exact, finite and regular class I solutions of Einstein’s field equations i.e. the solutions satisfy the Karmarkar condition. For this purpose needfully we have introduced a completely new suitable g_{rr} metric potential to generate the model. We have investigated the various physical aspects for our model such as energy density, pressure, anisotropy, energy conditions, equilibrium, stability, mass, surface and gravitational red-shifts, compactness parameter and their graphical representations. All these physical aspects have ensured that our proposed solutions are well-behaved and hence represent physically acceptable models for anisotropic fluid spheres. The models have satisfied causality and energy conditions. The presented models are also stable by satisfying Bondi condition and Abreu et al. condition, in equilibrium position and static by satisfying TOV equation, Harrison–Zeldovich–Novikov condition, respectively. For the parameters chosen in the paper are matching in modeling Vela X-1, Cen X-3, EXO 1785-248 and LMC X-4. The M–R graph generated from the solutions is matching the ranges of masses and radii for the considered compact stars. This work also estimated the approximate moment of inertia for the mentioned compact stars.