Charged Strange Stars Research Articles

Gravitational wave asteroseismology of charged strange stars in the Cowling approximation: the fluid pulsation modes

In this work we study, within the framework of Cowling approximation, the effect of the electric charge on the gravitational wave frequency of fluid oscillation modes of strange quark stars. For this purpose, the dense matter of the stellar fluid is described by the MIT bag model equation of state (EoS), while for the electric charge profile, we consider that the electric charge density is proportional to the energy density. We find that the gravitational wave frequencies change with the increment of electric charge; these effects are more noticeable at higher total mass values. We obtain that the f-mode is very sensitive to the change in the electric charge of the star. Furthermore, in the case of the p1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_1$$\\end{document} mode, the effect of the electric charge is not very significant. Our results reveal that the study of the fundamental pulsation mode of an electrically charged compact star is very important in distinguishing whether compact stars could contain electric charge. We also employ another electric charge distribution profile that follows a power law, and it is found that the f-mode change is more noticeable than the p1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_1$$\\end{document}-mode when the electric charge is incremented.

Charged analog of anisotropic dark energy star in Rastall gravity

Dark energy is one of the potential strategies for preventing compact objects from gravitationally collapsing into singularities. Because it is the cause of the accelerated expansion of our universe, it has the greatest impact on the cosmos. Thus, it is plausible that dark energy will interact with any stellar object that is compact in the universe [Phys. Rev. D 103 (2021) 084042]. Our main goal in this work is to create a simplified model, in the Rastall gravitational framework, of a charged strange star coupled to anisotropic dark energy in Krori–Barua spacetime [J. Phys. A, Math. Gen. 8 (1975) 508]. Here, we consider a specific strange star object, Her [Formula: see text], with observed values of mass [Formula: see text] and radius [Formula: see text] km, so that we can develop our model. In this context, we began by modeling dark energy using the equation of state (EoS), in which the dark energy density is proportional to the isotropic perfect fluid matter-energy density. The Darmois–Israel condition has been used to calculate the unknown constants that are present in the metric. We perform a detailed analysis of the model’s physical properties, including the mass–radius relation, pressure, density, metric function, and dark energy parameters for different Rastall coupling parameter values. We also examine the stability and force equilibrium of our proposed stellar configuration. Following a comprehensive theoretical analysis, we discovered that our suggested model is both singularity-free and meets all stability requirements needed to be a stable, physically reasonable stellar model.

Charged strange star coupled to anisotropic dark energy in Tolman–Kuchowicz spacetime

The concept of dark energy can be used as a possible option to prevent the gravitational collapse of compact objects into singularities. It affects the universe on the largest scale, as it is responsible for our universe’s accelerated expansion. As a consequence, it seems possible that dark energy will interact with any compact astrophysical stellar object [Phys. Rev. D 103, 084042 (2021)]. In this work, our prime focus is to develop a simplified model of a charged strange star coupled to anisotropic dark energy in Tolman–Kuchowicz spacetime (Tolman in Phys Rev 55:364, 1939; Kuchowicz in Acta Phys Pol 33:541, 1968) within the context of general relativity. To develop our model, here we consider a particular strange star object, Her X-1 with observed values of mass =(0.85 pm 0.15)M_{odot } and radius = 8.1_{-0.41}^{+0.41} km. respectively. In this context, we initially started with the equation of state (EoS) to model the dark energy, in which the dark energy density is proportional to the isotropic perfect fluid matter-energy density. The unknown constants present in the metric have been calculated by using the Darmois–Israel condition. We perform an in-depth analysis of the stability and force equilibrium of our proposed stellar configuration as well as multiple physical attributes of the model such as metric function, pressure, density, mass–radius relation, and dark energy parameters by varying dark energy coupling parameter alpha . Thus after a thorough theoretical analysis, we found that our proposed model is free from any singularity and also satisfies all stability criteria to be a stable and physically realistic stellar model.

Charged strange star model in Tolman–Kuchowicz spacetime in the background of 5D Einstein–Maxwell–Gauss–Bonnet gravity

In this article, we provide a new model of static charged anisotropic fluid sphere made of a charged perfect fluid in the context of 5D Einstein–Maxwell–Gauss–Bonnet (EMGB) gravity theory. To generate exact solutions of the EMGB field equations, we utilize the well-behaved Tolman–Kuchowicz (TK) ansatz together with a linear equation of state (EoS) of the form p_r=beta rho -gamma , (where beta and gamma are constants). Here the exterior space-time is described by the EGB Schwarzschild metric. The Gauss–Bonnet Lagrangian term mathcal {L}_{GB} is coupled with the Einstein–Hilbert action through the coupling constant alpha . When alpha rightarrow 0, we obtain the general relativity (GR) results. Here we present the solution for the compact star candidate EXO 1785-248 with mass=(1.3 pm 0.2)M_{odot }; radius = 10_{-1}^{+1} km. respectively. We analyze the effect of this coupling constant alpha on the principal characteristics of our model, such as energy density, pressure components, anisotropy factor, sound speed etc. We compare these results with corresponding GR results. Moreover, we studied the hydrostatic equilibrium of the stellar system by using a modified Tolman–Oppenheimer–Volkoff (TOV) equation and the dynamical stability through the critical value of the radial adiabatic index.The mass-radius relationship is also established to determine the compactness factor and surface redshift of our model. In this way, the stellar model obtained here is found to satisfy the elementary physical requirements necessary for a physically viable stellar object.

Charged strange stars with dust and phantom regimes in Rastall gravity

In this paper, we are focused on studying the possibility of providing a new well-behaved class of exact solutions for viable anisotropic stellar systems with dust and phantom regimes in the framework of Rastall gravity theory. This gravity theory modifies the matter sector only, incorporating new ingredients to the physical parameters that describe the model like charge density, electric field, density, and pressure components. Furthermore, other significant amounts are influenced, such as subliminal speeds of the pressure waves in radial and transversal directions, observational parameters such as the surface redshift associated with the total mass M and the radius R of the compact stellar configurations. Likewise, a transcendent mechanism such as equilibrium via generalized Tolman–Oppenheimer–Volkoff equation and stability of the stellar system is upset. The unidentified constraints are evaluated via the boundary conditions along with the dust and phantom models to describe as exterior space–times considering experimental statistics of five different stars i.e., EXO 1785 - 248, SMC X - 1, SAX J 1808.4 - 3658, 4U 1538 - 52, and HER X - 1. Various physical aspects have been analyzed with the help of modified dynamical equations. Exclusively, all the stellar configurations under observations are realistic, stable, and are free from all singularities. After witnessing the minor differences between our proposed models in both cases, Andréasson’s limit M≤R/3+R/9+Q2/3R has been fulfilled as required by the charged stellar structures. In such an astrophysical scenario, our new results provide circumstantial evidence in favor of super-massive pulsars.

Study on anisotropic charged strange stars within the framework of Rastall–Maxwell theory: Conformal Killing vector

The strange quark matter (SQM) for which the distribution is governed by the equation of state of the simplified MIT bag model such as: [Formula: see text], with [Formula: see text] the bag constant, in the presence of a load distribution given by [Formula: see text] has been the subject of a series of investigations within the framework of Rastall–Maxwell theory. We used the Modified Tolman–Oppenheimer–Volkoff (TOV) equation in Rastall gravity to generate the solutions by make using the conformal Killing vector. In order to check the physical acceptability of our solutions from conformal Killing vector method, we investigated around the Energy conditions, the Mass–Radius relation, Modified TOV equation, redshift and the stability of the system through Adiabatic Index, the Compactification factor and Causality condition. For physical values of Rastall parameters, we noticed that the stellar systems become more massive in proportion to their size. Then, this leads them into less dense compact objects which reveals that the alternative theory of Rastall is appropriate to better explain the behavior of massive stellar objects.

Charged strange star in $f(R,T)$ gravity with linear equation of state

Our present study involves the strange stars model in the framework of $f(R,T)$ theory of gravitation. We have taken a linear function of the Ricci scalar $R$ and the trace $T$ of the stress-energy tensor $T_{\mu \nu}$ for the expression of $f(R,T)$, i.e., $f(R,T)=R+ 2 \gamma T $ to obtain the proposed model, where $\gamma$ is a coupling constant. Moreover, to solve the hydrostatic equilibrium equations, we consider a linear equation of state between the radial pressure $p_r$ and matter density $\rho$ as $p_r=\alpha \rho-\beta$, where $\alpha$ and $\beta$ are some positive constants, Both $\alpha,\,\beta$ depend on coupling constant $\gamma$ which have been also depicted in this paper. By employing the Krori-Barua {\em ansatz} already reported in the literature [J. Phys. A, Math. Gen. 8:508, 1975] we have found the solutions of the field equations in $f (R, T )$ gravity. The effect of coupling constant $\gamma$ have been studied on the model parameters like density, pressures, anisotropic factor, compactness, surface redshift, etc. both numerically and graphically. A suitable range for $\gamma$ is also obtained. The physical acceptability and stability of the stellar system have been tested by different physical tests, e.g., the causality condition, Herrera cracking concept, relativistic adiabatic index, energy conditions, etc. One can regain the solutions in Einstein gravity when $\gamma\rightarrow 0$

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

We present spherically symmetric anisotropic charged strange stars under the framework of f(R,T) gravity. For this we consider that the Lagrangian density is a linear function of R and T where R is the Ricci Scalar and T represents the trace of the energy–momentum tensor. These stars are considered to be built with Strange Quark Matter (SQM) distribution. To describe this SQM distribution inside the stellar bodies, we incorporate the simplest form of phenomenological MIT bag model equation of state (EOS) pr=13(ρ−4Bg), where pr is the radial pressure, ρ is the energy density and Bg is the bag constant. To determine density and pressure from the Einstein Field Equations (EFE), we use Krori-Barua (KB) metric and using the observed values of mass and radius for strange star candidates LMCX−4, we calculate the value of Bg from our model. Comparing the interior metric with exterior Reissner-Nordström metric at the surface, we calculate the unknown parameters incorporating the observed values of the mass and radius, we find that the coupling constant χ affects the bag value significantly. The model shows consistency with all the physical conditions and presents a viable study to the nature of charged anisotropic massive stellar system.

Charged strange star with Krori–Barua potential in f(R, T) gravity admitting Chaplygin equation of state

In present paper a new compact star model in f(R,T) gravity is obtained where R and T denote the Ricci scalar and the trace of energy-momentum tensor $T_{\mu \nu}$ respectively. To develop the model we consider the spherically symmetric space-time along with anisotropic fluid distribution in presence of electric field with $f(R,T) = R + 2\gamma T$ where $\gamma$ is a small positive constant. We have used the Chaplygin equation of state to explore the stellar model. The field equations for $f(R,T)$ gravity have been solved by employing the Krori-Barua ansatz already reported in literature [J. Phys. A, Math. Gen. 8:508, 1975]. The exterior spacetime is described by Reissner-Nordstrom line element for smooth matching at the boundary. It is worthwhile to mention here that the values of all the constants involved with this model have been calculated for the strange stars 4U 1538-52 for different values of {\gamma} with the help of matching conditions. The acceptability of the model is discussed in details both analytically and graphically by studying the physical attributes of matter density, pressures, anisotropy factor, stability etc. We have also obtained the numerical values in tabular form for central density, surface density, central pressure and central adiabatic index for different values of $\gamma$. The solutions of the field equations in Einstein gravity can be regained by simply putting $\gamma = 0$ to our solution. Moreover, the proposed model is shown to be physically admissible and corroborate with experimental observations on strange star candidates such as 4U 1538-52.

Electrically charged strange stars with an interacting quark matter equation of state

The properties of electrically charged strange quark stars predicted by an interacting quark matter equation of state (EoS) based on cold and dense perturbative quantum chromodynamics (pQCD) are investigated. The stability of strange stars is analyzed considering different models for the electric charge distribution inside the star as well as for distinct values for the total electric charge. A comparison with the predictions derived using the MIT bag model is also presented. We show that the presence of a net electric charge inside strange stars implies in a larger maximum mass in comparison to their neutral counterparts. Moreover, we demonstrate that the pQCD EoS implies larger values for the maximum mass of charged strange stars, with very heavy charged stars being stable systems against radial oscillations. For an electric charge distribution given by $q(r) = \beta r^3$, the pQCD EoS implies unstable configurations for large values of the renormalization scale as well as for large values of $\beta$, in contrast to the MIT bag model predictions.

Study on charged strange stars in f(R, T) gravity

We investigate the effects of the modified f(R, T) gravity on the charged strange quark stars with the standard choice of f(R, T)=R+2χ T. Those types of stars are supposed to be made of strange quark matter (SQM) whose distribution is governed by the phenomenological MIT bag EOS as p=1/3(ρ−4B), where B is the bag constant, while the form of charge distribution is chosen to be q(r)=Q(r/ℛ)3=α r3 with α as a constant. We derive the values of the unknown parameters by matching the interior spacetime to the exterior Reissner-Nordstr{öm metric followed by the appropriate choice of the values of the parameters χ and α. Our study reveals that besides SQM, a new kind of matter distribution originates due to the interaction between the matter and the extra geometric term, while the modification of the Tolman-Oppenheimer-Volkoff (TOV) equation invokes the presence of a new force Fc. The accumulation of the electric charge distribution reaches its maximum at the surface, and the predicted values of the corresponding electric charge and electric field are of the order of 1019−20C and 1021−22 V/cm, respectively. To examine the physical validity of our solutions, we perform tests of the energy conditions, stability against the equilibrium of the forces, the adiabatic index, etc., and find that the proposed f(R, T) model survives all these critical tests. Therefore, our model can describe the non-singular charged strange stars and justify the supermassive compact stellar objects having their masses beyond the maximum mass limit for the compact stars in the standard scenario. Our model also supports the existence of several exotic astrophysical objects like super-Chandrasekhar white dwarfs, massive pulsars, and even magnetars, which remain unexplained in the framework of General Relativity (GR).

Charged anisotropic strange stars in Finslerian geometry

We investigate a simplified model of the strange stars in the framework of Finslerian geometry, composed of charged fluid. It is considered that the fluid consisting of three flavor quarks including a small amount of non-interacting electrons to maintain the chemical equilibrium and assumed that the fluid is compressible by nature. To obtain the simplified form of the charged strange star we have considered constant flag curvature. Based on geometry, we have developed the field equations within the localized charge distribution. We consider that the strange quarks distributed within the stellar system are complied with the MIT bag model type of equation of state (EOS) and the charge distribution within the system follows a power law. We represent the exterior spacetime by the Finslerian Ressiner-Nordström space-time. The maximum anisotropic stress is obtained at the surface of the system. Whether the system is in equilibrium or not, has been examined with respect to the Tolman–Oppenheimer–Volkoff (TOV) equation, Herrera cracking concept, different energy conditions and adiabatic index. We obtain that the total charge is of the order of 10^{20}hbox { C} and the corresponding electric field is of around 10^{22}hbox { V/m}. The central density and central pressure vary inversely with the charge. Varying the free parameter (charge constant) of the model, we find the generalized mass-radius variation of strange stars and determine the maximum limited mass with the corresponding radius. Furthermore, we also considered the variation of mass and radius against central density respectively.

Radial oscillations of charged strange stars

The radial oscillations of charged strange quark stars is investigated. It is considered that the fluid pressure follows the MIT bag model equation of state and the charge density to be proportional to the energy density, ρe = αρ (where α is proportionality constant). The modified equations of radial oscillations to the introduction of the electric charge are integrated to determine the fundamental mode. It is found that the stability of the charged object decreases with the increment of the central energy density and with the growth of the charge fraction.

Some analytical models of anisotropic strange stars

Over the years of the concept of local isotropy has become a too stringent condition in modeling relativistic self-gravitating objects. Taking local anisotropy into consideration, in this work, some analytical models of relativistic anisotropic charged strange stars have been developed. The Einstein–Maxwell gravitational field equations have been solved with a particular form of one of the metric potentials. The radial pressure and the energy density have been assumed to follow the usual linear equation of state of strange quark matter, the MIT bag model.

Equilibrium and stability of charged strange quark stars

The hydrostatic equilibrium and the stability against radial perturbation of charged strange quark stars composed of a charged perfect fluid are studied. For this purpose, it is considered that the perfect fluid follows the MIT bag model equation of state and the radial charge distribution follows a power-law. The hydrostatic equilibrium and the stability of charged strange stars are investigated through the numerical solutions of the Tolman-Oppenheimer-Volkoff equation and the Chandrasekhar's pulsation equation, being these equations modified from their original form to include the electrical charge. In order to appreciably affect the stellar structure, it is found that the total charge should be of order $10^{20}[\rm C]$, implying an electric field of around $10^{22}[\rm V/m]$. We found the electric charge that produces considerable effect on the structure and stability of the object is close to the star's surface. We obtain that for a range of central energy density the stability of the star decreases with the increment of the total charge and for a range of total mass the electric charge helps to grow the stability of the stars under study. We show that the central energy density used to reach the maximum mass value is the same used to determine the zero eigenfrequency of the fundamental mode when the total charge is fixed, thus indicating that the maximum mass point marks the onset of instability. In other words, when fixing the total charge, the conditions $\frac{dM}{d\rho_c}>0$ and $\frac{dM}{d\rho_c}<0$ are necessary and sufficient to determine the stable and unstable equilibrium configurations regions against radial oscillations.