Tolman-Oppenheimer-Volkoff Equations Research Articles

Conserved charges in general relativity

We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved space–time with Killing vectors. This definition enables us to define energy and momentum for matter by the volume integral. As a result we can compute charges of Schwarzschild and BTZ black holes by the volume integration of a delta function singularity. Employing the definition we also compute the total energy of a static compact star. It contains both the gravitational mass known as the Misner–Sharp mass in the Oppenheimer–Volkoff equation and the gravitational binding energy. We show that the gravitational binding energy has the negative contribution at maximum by 68% of the gravitational mass in the case of a constant density. We finally comment on a definition of generators associated with a vector field on a general curved manifold.

Anisotropic spherical solutions via EGD using isotropic Durgapal–Fuloria model

Our main focus is to calculate analytic solutions for spherically symmetric self-gravitating systems using anisotropic fluid via decoupling technique dubbed as extended gravitational decoupling (EGD) approach. To this end, we choose an isotropic Durgapal–Fuloria solution and generalize it to anisotropic domain by transforming temporal and radial metric potentials. We check stability and physical viability of the obtained anisotropic interior solutions via graphical trajectories of energy conditions, TOV equation, causality constraints as well as adiabatic index for the compact stars namely PSR J 1416-2230 and Her X-I. It is found that both of the stellar models exhibit feasible realistic behavior fulfilling all the physical constraints and stability criterion. Hence, the EGD technique is more efficient to explain the interior structure of the stellar objects.

Neutron stars phenomenology with scalar–tensor inflationary attractors

In this work we shall study the implications of a subclass of E -models cosmological attractors, namely of a -attractors, on hydrodynamically stable slowly rotating neutron stars. Specifically, we shall present the Jordan frame theory of the a -attractors, and by using a conformal transformation we shall derive the Einstein frame theory. We discuss the inflationary context of a -attractors in order to specify the allowed range of values for the free parameters of the model based on the latest cosmic-microwave-background-based Planck 2018 data. Accordingly, using the notation and physical units frequently used in theoretical astrophysics contexts, we shall derive the Tolman–Oppenheimer–Volkoff equations in the Einstein frame. Assuming a piecewise polytropic equation of state, the lowest density part of which shall be chosen to be the WFF1, or APR or the SLy EoS, we numerically solve the Tolman–Oppenheimer–Volkoff equations using a double shooting python-based “LSODA” numerical code. The resulting picture depends on the value of the parameter a characterizing the a -attractors. As we show, for large values of a , which do not produce a viable inflationary era, the M – R graphs are nearly identical to the general relativistic result, and these two are discriminated at large central densities values. Also, for large a -values, the WFF1 equation of state is excluded, due to the GW170817 constraints on the radius of an M ∼ 1 . 6 M ⊙ neutron star, which must be larger than R = 10 . 6 8 − 0 . 04 + 15 km and on the radius corresponding to the maximum mass which must be larger than R = 9 . 6 − 0 . 03 + 0 . 14 km. In addition, the small a cases produce larger masses and radii compared to the general relativistic case and are compatible with the GW170817 constraints on the radii of neutron stars. A notable feature is that as the parameter a decreases, the radii of the static hydrodynamically stable neutron stars increase. Our results indicate deep and not yet completely understood connections between non-minimal inflationary attractors and neutron stars phenomenology in scalar–tensor theory.

Classification theorem and properties of singular solutions to the Tolman–Oppenheimer–Volkoff equation

The Tolman–Oppenheimer–Volkoff (TOV) equation admits singular solutions in addition to regular ones. Here, we prove the following theorem. For any equation of state that (i) is obtained from an entropy function, (ii) has positive pressure and (iii) satisfies the dominant energy condition, the TOV equation can be integrated from a boundary inwards to the center. Hence, the thermodynamic consistency of the EoS precludes pathological solutions in which the integration terminates at finite radius (because of horizons, or divergences / zeroes of energy density). At the center, the mass function either vanishes (regular solutions) or it is negative (singular solutions). For singular solutions, the metric at the center is locally isomorphic to negative-mass Schwarzschild spacetime. This means that matter is stabilized because the singularity is strongly repulsive. We show that singular solutions are causally well behaved: they are bounded-acceleration complete, and they are conformal to a globally hyperbolic spacetime with boundary. Finally, we show how to modify unphysical equations of state in order to obtain non-pathological solutions, and we undertake a preliminary investigation of dynamical stability for singular solutions.

Strange Quark Stars in 4D Einstein–Gauss–Bonnet Gravity

Abstract The existence of strange matter in compact stars may give rise to striking outcomes of the various physical phenomena. As an alternative to neutron stars, a new class of compact stars called strange stars should exist if the strange matter hypothesis is true. In this paper, we investigate the possible construction of strange stars in quark matter phases based on the MIT bag model. We consider scenarios in which strange stars have no crusts. Then we apply two types of equations of state to quantify the mass–radius diagram for static strange star models, performing the numerical calculation of the modified Tolman–Oppenheimer–Volkoff equations in the context of 4D Einstein–Gauss–Bonnet (EGB) gravity. It is worth noting that the GB term gives rise to a nontrivial contribution to the gravitational dynamics in the limit D → 4. However, the claim that the resulting theory is one of pure gravity has been cast in doubt on several grounds. Thus, we begin our discussion by showing the regularized 4D EGB theory has an equivalent action as the novel 4D EGB in a spherically symmetric spacetime. We also study the effects of coupling constant α on the physical properties of the constructed strange stars including the compactness and criterion of adiabatic stability. Finally, we compare our results to those obtained from standard general relativity.

A new parametric class of solutions of a charged anisotropic compact star via Bardeen exterior geometry

In this paper, we provide a new parametric class of solutions to Einstein–Maxwell field equations to study the relativistic structure of a compact star via embedding class I condition. The interior of the star is delineated by Karmarkar condition and at the boundary of the star, we match the class of solutions with Bardeen and Reissner–Nordstrom exterior spacetimes. We assume one of the metric potentials as [Formula: see text] to obtain other metric potential. Subsequently, we solve Maxwell field equations. We verify and compare all the thermodynamic properties like matter density, anisotropy, radial and tangential pressures, compactification factor, energy conditions, and stability conditions, namely, adiabatic index, balancing forces via modified TOV equations, Harrision–Zeldovich criteria, casualty condition, Herrera cracking condition, etc., of our class of charged solutions. All the physical and stability conditions are with the viable trend throughout the interior of the stellar object. For a suitable range of values of [Formula: see text] and parameters, it is depicted from this study that the present class of charged solutions yields effective results to obtain realistic and viable modeling of the neutron star in EXO 1785-248 in both the Bardeen and Reissner–Nordstrom exterior spacetimes.

TOV equations form of anisotropic pressure on two fluid models

We construct Tolman Oppenheimer Volkoff (TOV) equations for anisotropic pressure of two non-interacted perfect fluid with different four-velocities. This paper’s primary motivation is that we obtain the result that could describe the neutron stars (NS) admixed with dark matter (DM) that satisfying constraint from GW190814. Otherwise, our result also can investigate other compact objects that are admixed with two non-interacting fluids. In this work, we extend the formalism in Ref [1] by considering each fluid’s anisotropic pressure. Therefore, the total energy-momentum tensor is the sum of two non-interacting anisotropic fluids with different four-velocities. The velocity difference of both fluids denotes here by b where it comes from each of four-velocities under transformation rotation. Our result’s direct impact is that we can assess each fluid’s impact of anisotropic pressure in two fluids formalism in NS or other compact objects properties.

Compact objects in f(R, T) gravity with Finch–Skea geometry

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.

Radial oscillations and gravitational wave echoes of strange stars for various equations of state

ABSTRACT 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.

Anisotropic models for compact star with various equation of state

We model anisotropic compact stars by solving Einstein field equation with a generalized form of equation of state (EoS) and a physically reasonable metric potential $$g_{rr}$$ which allows us to extract models with various type of EoSs such as linear, quadratic, polytrope, Chaplygin and Color-flavor-locked. The generated interior metrics match smoothly with the exterior Schwarzschild metric. The radius $$R = 8.301$$ km and mass $$M=1.0359M_{\odot }$$ of the strange star candidate SMC X-1 has been used as reference to check the physical validity of the generated models. The physical quantities emanating from the analysis for all generated models are regular and well behaved throughout the interior of the star and satisfy the necessary criterion of a realistic anisotropic star. The significance of EoSs in modeling a realistic star with regard to its gross physical behavior has been illustrated by graphical analysis. A complete physical analysis has been performed for the main physical observables, such as the density $$\rho $$ , the radial and tangential pressures as well as the anisotropy factor. Moreover, the stability of the star has been checked by means of the velocities of the pressure waves and the relativistic adiabatic index. The generated models satisfy the Bondi’s stability condition and Tolman–Oppenheimer–Volkoff equation for static equilibrium for all type of EoSs. The effect of anisotropy on cracking condition has been discussed.

A model of compact and ultracompact objects in f(mathcal {R})-Palatini theory

We present the features of a model which generalizes Schwarzschild’s homogeneous star by adding a transition zone for the density near the surface. By numerically integrating the modified TOV equations for the f(mathcal {R})=mathcal {R}+lambda mathcal {R}^2 Palatini theory, it is shown that the ensuing configurations are everywhere finite. Depending on the values of the relevant parameters, objects more, less or as compact as those obtained in GR with the same density profile have been shown to exist. In particular, in some region of the parameter space the compactness is close to that set by the Buchdahl limit.

Modeling of anisotropic spheres in extended teleparallel theory with matter coupling

This work is devoted to investigate the structures of compact stars by using spherically static symmetric space-time in the background of f(τ,T) gravity, where τ represents the torsion scalar and T represents the trace of the energy momentum tensor. We develop the field equations by using the concept of quintessence to discuss the motion by using anisotropic fluid distribution with a spherically symmetric metric. We use the convention of junction conditions to evaluate the unknown parameters used in the study of the compact stars. In this study we use the available data of three different compact objects 4U1608−52,CenX−3 and EXO1785−240. We discuss the physical and analytical existence of compact stars by satisfying some standard properties of compact stars like the behavior of the energy density, quintessence density, radial and tangential pressures, anisotropy, to elaborate the anisotropic nature of the star. We discuss the sound speeds and casuality conditions to show the stability of the system. Equilibrium of the star is justified by the TOV equation. Red-shift function, compactness, and mass function states the physical existence of the star. It is examined that all these parameters show the viability and stability of the model used in the effects of f(τ,T) gravity.

Charged strange stellar model describing by Tolman V metric

This paper deals with the existence of a compact stellar object, precisely strange (quark) star, in the framework of Einstein’s General Theory of Relativity with Tolman V metric potential, which is one of the simplest forms of potential among his proposals. The potential is given by eν=Kr2n, where K is the constant and n is a parameter [R.C. Tolman, Phys. Rev. 55, 364 (1939)]. Considering charged, static, spherically symmetric, isotropic fluid sphere we have studied different physical features of some strange star candidates namely EXO1785-248,LMCX-4,SMCX-1,SAXJ1808.4-3658,4U1538-52 and HerX-1. To represent the strange quark matter (SQM) distribution we have employed the simplest form of MIT Bag equation of state (EOS), which provides a linear relationship between pressure and density of the matter through Bag constant B. Several tests are done for the stability criteria and physical acceptability of the proposed model. The results show consistency with energy condition, TOV equation, adiabatic index, etc. We have also calculated different physical parameters of our model for the three different consecutive values of Bag constant B which are 83MeV/fm3,90MeV/fm3 and 100MeV/fm3. Among them with B=90MeV/fm3 we have analyzed different properties of the proposed strange star candidates.

Massive compact Bardeen stars with conformal motion

The main focus of this paper is to discuss the solutions of Einstein-Maxwell's field equations for compact stars study. We have chosen the MIT Bag model equation of state for the pressure-energy density relationship and conformal Killing vectors are used to investigate the appropriate forms for metric coefficients. We impose the boundary conditions, by choosing the Bardeen model to describe as an exterior spacetime. The Bardeen model may provide the analysis with some interesting results. For example, the extra terms involved in the asymptotic representations as compared to the usual Reissner-Nordstrom case may influence the mass of a stellar structure. Both energy density and pressure profiles behave realistically except a central singularity. It is shown that the energy conditions are satisfied in our study. The equilibrium conditions through TOV equation and stability criteria through Adiabatic index for the charged stellar structure study are investigated. We have also provided a little review of the case with Reissner-Nordstrom spacetime as an exterior geometry for the matching condition. In both cases, the masses obey the Andreasson's limit M≤R/3+R/9+q2/3R requirement for a charged star. Conclusively, the results show that Bardeen model geometry provides more massive stellar objects as compared to usual Reissner-Nordstrom spacetime. In particular, the current study supports the existence of realistic massive structures like PSR J 1614−2230.

Compact stars with variable cosmological constant in $f(\mathcal{R,T})$ gravity

This paper explores and analyzes a set of solutions describing the interior structure of relativistic compact stellar structures with variable cosmological constant $\Lambda (r)$ . We consider the solution of Krori–Barua space-time to a static spherical symmetric metric. Furthermore, we match our interior stellar structure with the exterior Schwarzschild geometry to determine the values of the constants used in the solution of the Krori–Barua space-time. The numerical values of these constants were determined for a set of different compact stars, and using these constants in our solutions, we have studied the viability of matter content, stability, TOV equations, and surface red-shift; and we predicted some physical aspects like central and surface densities, stresses, masses, and radii.

A study of anisotropic spheres in modified gravity via embedding approach

The motivation of this paper is based on the foundation of extended teleparallel gravity with matter coupling to prospect the accelerated expansion of the Universe. This theory based on the torsion scalar along with the trace term of energy stress tensor. We manipulate the spherical symmetric metric and anisotropic fluid to discuss the study of stellar structures. To interpret our research, we used the observational data of three stars. We adopt the process of parallelism of interior and exterior space-times to estimate the unspecified parameters used in the stellar discussion. Further, we discuss the stellar properties like energy density, progressive behavior of radial and tangential components of pressure, the anisotropic formation of the compact stars. We also analyze the physical presence of stars by discussing the energy conditions redshift and mass functions. We signify the stability of the system by examining the speed of sounds and EoS. We show the equilibrium of the system by analyzing the TOV equation. Finally, we show that our system in the discussion is physically stable and analytically viable.

Anisotropic spheres in [formula omitted]gravity with Tolman-Kuchowicz spacetime

In this paper, we review some anisotropic stellar spheres in the framework of modified f(R,G)gravity. For this purpose, we have capitalized the Tolman-Kuchowicz spacetime Tolman (1939); Kuchowicz (1968). The equations of motion have been formulated by considering anisotropic matter distribution along with metric potentials, a=Br2+2lnCand b=ln(1+αr2+βr4). To determine the new constraints, observational data of 4U1538−52,HerX−1and SAXJ1808.4−3658have been pre-owned. Dynamical equations have been evaluated by making use of Starobinsky model f(R,G)=R+λR2+G2. Many physical aspects have been enlightened, such as energy density, pressure evolutions, adiabatic index, TOV equations and surface redshift. The credibility of our presented model has been confirmed by observing the evolution of some physical aspects and it is concluded that our system is free from all singularities and is physically stable.

Stable and self-consistent compact star models in teleparallel gravity

In the framework of Teleparallel Gravity, we derive a charged non-vacuum solution for a physically symmetric tetrad field with two unknown functions of radial coordinate. The field equations result in a closed-form adopting particular metric potentials and a suitable anisotropy function combined with the charge. Under these circumstances, it is possible to obtain a set of configurations compatible with observed pulsars. Specifically, boundary conditions for the interior spacetime are applied to the exterior Reissner–Nordström metric to constrain the radial pressure that has to vanish through the boundary. Starting from these considerations, we are able to fix the model parameters. The pulsar textit{PSR J 1614-2230}, with estimated mass M= 1.97 pm 0.04, M_{circledcirc }, and radius R= 9.69 pm 0.2 km is used to test numerically the model. The stability is studied, through the causality conditions and adiabatic index, adopting the Tolman–Oppenheimer–Volkov equation. The mass–radius (M, R) relation is derived. Furthermore, the compatibility of the model with other observed pulsars is also studied. We reasonably conclude that the model can represent realistic compact objects.

Exploring physical properties of compact stars in f(R,T)-gravity: An embedding approach

Solving field equations exactly in gravity is a challenging task. To do so, many authors have adopted different methods such as assuming both the metric functions and an equation of state (EoS) and a metric function. However, such methods may not always lead to well-behaved solutions, and the solutions may even be rejected after complete calculations. Nevertheless, very recent studies on embedding class-one methods suggest that the chances of arriving at a well-behaved solution are very high, which is inspiring. In the class-one approach, one of the metric potentials is estimated and the other can be obtained using the Karmarkar condition. In this study, a new class-one solution is proposed that is well-behaved from all physical points of view. The nature of the solution is analyzed by tuning the coupling parameter , and it is found that the solution leads to a stiffer EoS for than that for . This is because for small values of , the velocity of sound is higher, leading to higher values of in the curve and the EoS parameter . The solution satisfies the causality condition and energy conditions and remains stable and static under radial perturbations (static stability criterion) and in equilibrium (modified TOV equation). The resulting diagram is well-fitted with observed values from a few compact stars such as PSR J1614-2230, Vela X-1, Cen X-3, and SAX J1808.4-3658. Therefore, for different values of , the corresponding radii and their respective moments of inertia have been predicted from the curve.

Anisotropic fluid spheres admitting Karmarkar condition in [formula omitted] gravity

This study deals with the construction of compact stars in f(G,T) gravity, where T and G represent the trace of energy momentum tensor and Gauss-Bonnet term respectively. We consider spherically symmetric space-time with anisotropic fluid distribution. In particular, the Karmarkar condition to embed the spherically symmetric space-time into class-1 metric is used to explore the compact stars solutions. Further, we choose two specific sets of observational data, like LMC X-4 (mass =1.29M/M⊙ & radii=9.711 km), and EXO 1785-248 (mass =1.30M/M⊙ & radii=8.849 km). The paper can be divided mainly in two parts. Firstly, we construct the modified filed equations for f(G,T) gravity by imposing the Karmarkar condition. By matching the exterior Schwarzschild spacetime with interior space-time metric at the boundary and taking the values of radii and masses of LMC X-4 and EXO 1785-248, we have calculated the different values of the parameter K. We provide a detail graphical analysis of the physical acceptability of important features, i.e., energy density, pressure, anisotropy, and gradients. We have also shown the stability of the stellar structures by employing the energy conditions, equation of state, generalized TOV equation, causality condition, and adiabatic index. For current analysis, we estimate some numerical values in tabular form for central density, central gravitational metric functions and central pressures components. We have also calculated the ratio prc/ρc=ptc/ρc, which has satisfied the Zeldovich’s condition. Conclusively, obtained results suggest that f(G,T) gravity supports anisotropic fluid spheres in the background of Karmarkar condition.