Compact Stellar Model with Two Different Equations of State

In this article, we investigate the properties of neutron stars within the braneworld model, employing six distinct piece-wise polytropic equation of states. These equation of states satisfy observational constraints put by GW170817 event and pulsar observations (PSR J0740 and PSR J0030) within general relativity framework. Our primary goal is to assess whether these equation of states, in conjunction with the braneworld framework, can accommodate more massive neutron stars, as suggested by the GW190814 observation, while remaining consistent with established observational constraints. The brane tension parameter significantly affects the mass-radius and mass-tidal deformability relations, particularly for neutron stars with masses exceeding the canonical value. We establish strong constraints on the brane tension by comparing the canonical neutron star radius and tidal deformability with the results from the braneworld model, a stringent lower bound on the brane tension, $$\lambda > 2 \times 10^{37} \, \text{ dyne/cm } ^2 $$ λ > 2 × 10 37 dyne/cm 2 . Our results demonstrate that the braneworld model allows for the existence of neutron stars with masses greater than those predicted by General Relativity, in agreement with the GW190814 observation, and highlight the significant role of brane tension in shaping the properties of neutron stars.

We present results from three-dimensional general relativistic simulations of binary neutron star coalescences and mergers using public codes. We considered equal mass models where the baryon mass of the two neutron stars is , described by four different equations of state (EOS) for the cold nuclear matter (APR4, SLy, H4, and MS1; all parametrized as piecewise polytropes). We started the simulations from four different initial interbinary distances (, and 60 km), including up to the last 16 orbits before merger. That allows us to show the effects on the gravitational wave (GW) phase evolution, radiated energy and angular momentum due to: the use of different EOS, the orbital eccentricity present in the initial data and the initial separation (in the simulation) between the two stars. Our results show that eccentricity has a major role in the discrepancy between numerical and analytical waveforms until the very last few orbits, where ‘tidal’ effects and missing high-order post-Newtonian coefficients also play a significant role. We test different methods for extrapolating the GW signal extracted at finite radii to null infinity. We show that an effective procedure for integrating the Newman–Penrose signal to obtain the GW strain h is to apply a simple high-pass digital filter to h after a time domain integration, where only the two physical motivated integration constants are introduced. That should be preferred to the more common procedures of introducing additional integration constants, integrating in the frequency domain or filtering before integration.

New solution for the Einstein field equations satisfying a neutral anisotropic quark star object is generated. The quark linear equation of state together with the conformal Killing vector (CKV) are used to investigate the behavior and properties of quark stars. The CKV plays an important role in providing the relationship between the two gravitational potentials. The process of combining the CKV and an equation of state has currently led to new realistic solutions. In obtaining the matter variables, one of the gravitational potentials is specified on physical grounds to generate compact star model with physical significance. The generated quark star model undergoes several physical tests for the validity and acceptability. Several realistic physical conditions are found to be satisfied. The model stability in terms of the adiabatic index and equilibrium of the physical forces is satisfied. The behavior of the mass-radius relationship and the surface red shift are well obeyed. Their parameters values are found to be compatible with observations. The gravitational potentials are continuous throughout the interior of the star, and the model's energy conditions are satisfied as well. Quark star models that admit conformal symmetry in the absence of charge are missing in the existing literature.

Effects of Different Equations of State on the Oblique Shock Wave Reflection in Solids

In this study, our aim is to generate the new anisotropic solution for compact stellar configurations with the help of Buchdahl geometry. We used the Buchdahl metric potential [J. Astrophys. Astron. 3, 325 (1982)] to deal with the field equations in general relativity framework. To get the constant parameters, the exterior Schwarzschild de Sitter solution is linked to the interior solution at the boundary. We discuss the behavior of density, radial and tangential pressure for the present model. We take the star candidates 4U 1820-30, PSR J1903+327, 4U 1608-52, 4U 1538-52 and HerX-1 to complete our analysis. The proposed compact stars equilibrium and stability states are analyzed using the Tolman-Oppenheimer-Volkoff equation, causality condition, adiabatic index and Harrison-Zeldovich-Novikov Criterion, respectively. It is noticed that our proposed model is suitable and provides viable results with Buchdahl geometry.

In this work, we present a general framework for obtaining exact solutions to the symmetric teleparallel gravity field equations describing strange stars obeying a colour-flavour-locked (CFL) equation of state. This study examines four star candidates: PSR J1614-2230, RXJ1856-37, HER X-1, and SAX J1808-3658. These stars have masses of 1.3 M ⊙ , 0.9031 M ⊙ , 0.98 M ⊙ , and 0.9 M ⊙ , respectively, and radii of 7.259 km, 6 km, 6.7 km, and 7.26 km, respectively. In our study, we solve the f(Q) gravity field equations by assuming a specific metric ansatz g rr component, and evaluate the g tt component by using the colour-flavour-locked (CFL) equation of state. We calculate the exterior spacetime using the principle of f(Q) gravity. The matching of the interior solution with that of the exterior spacetime is employed to determine the model parameters for given realistic compact stars. In this research, we study some properties of stellar models such as the behavior of the density and pressure components, the energy conditions, the metric components, the equation of state components, the sound speeds, the adiabatic index, the gradients, the mass function, the compactness, and the redshift function. Additionally, we examine the stability and equilibrium of the proposed stellar configuration. Our detailed theoretical analysis justifies the realism and feasibility of the stellar configuration considered by demonstrating that the proposed model is free of singularities and satisfies all stability requirements.

The possibility of observationally discriminating between various types of neutron stars, described by different equations of state of the nuclear matter, as well as differentiating neutron stars from other types of exotic objects, like, for example, quark stars, is one of the fundamental problems in contemporary astrophysics. We consider and investigate carefully the possibility that different types of rapidly rotating neutron stars, as well as other type of compact general relativistic objects, can be differentiated from the study of the emission properties of the accretion disks around them. We obtain the energy flux, the temperature distribution and the emission spectrum from the accretion disks around several classes of rapidly rotating neutron stars, described by different equations of state of the neutron matter, and for quark stars, described by the MIT bag model equation of state and in the CFL (Color-Flavor-Locked) phase, respectively. Particular signatures appear in the electromagnetic spectrum, thus leading to the possibility of directly testing the equation of state of the dense matter by using astrophysical observations of the emission spectra from accretion disks.

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.

A set of unified relativistic mean-field equations of state for hyperonic compact stars recently built in [M. Fortin, Ad. R. Raduta, S. Avancini, and C. Providencia, Phys. Rev. D {\bf 101}, 034017 (2020)] is used to study the thermal evolution of non-magnetized and non-rotating spherically-symmetric isolated and accreting neutron stars under different hypothesis concerning proton $S$-wave superfluidity. These equations of state have been obtained in the following way: the slope of the symmetry energy is in agreement with experimental data; the coupling constants of $\Lambda$ and $\Xi$-hyperons are determined from experimental hypernuclear data; uncertainties in the nucleon-$\Sigma$ interaction potential are accounted for; current constraints on the lower bound of the maximum neutron star mass are satisfied. Within the considered set of equations of state, the presence of hyperons is essential for the description of the cooling/heating curves. One of the conclusions we reach is that the criterion of best agreement with observational data leads to different equations of states and proton $S$-wave superfluidity gaps when applied separately for isolated neutron stars and accreting neutron stars in quiescence. This means that at least in one situation the traditional simulation framework that we employ is not complete and/or the equations of state are inappropriate. Another result is that, considering equations of state which do not allow for nucleonic dUrca or allow for it only in very massive NS, the low luminosity of SAX J1808 requires a repulsive $\Sigma$-hyperon potential in symmetric nuclear matter in the range $U_\Sigma^{(N)}\approx 10-30$ MeV. This range of values for $U_\Sigma^{(N)} $ is also supported by the criterion of best agreement with all available data from INS and XRT.

Spherically symmetric relativistic stars with the polytropic equation of state (EoS), which possess the local pressure anisotropy, are considered within the framework of general relativity. The generalized Lane-Emden equations are derived for the arbitrary anisotropy parameter $\Delta=p_t-p_r$ ($p_t$ and $p_r$ being the transverse and radial pressure, respectively). They are then applied to some special ansatz for the anisotropy parameter in the form of the differential relation between the anisotropy parameter $\Delta$ and the metric function $\nu$. The analytical solutions of the obtained equations are found for incompressible fluid stars and then used for getting their mass-radius relation, gravitational and binding energy. Also, following the Chandrasekhar variational approach, the dynamical stability of incompressible anisotropic fluid stars with the polytropic EoS against radial oscillations is studied. It is shown that the local pressure anisotropy with $p_t>p_r$ can make the incompressible fluid stars unstable with respect to radial oscillations, in contrast to incompressible isotropic fluid stars with the polytropic EoS which are dynamically stable.

Pure hadronic compact stars, above a limiting value ($\\approx$1.6 M$_\\odot$)\nof their gravitational masses, to which predictions of most of other equations\nof state (EoSs) are restricted, can be reached from the equation of state (EoS)\nobtained using DDM3Y effective interaction. This effective interaction is found\nto be quite successful in providing unified description of elastic and\ninelastic scattering, various radioactivities and nuclear matter properties. We\npresent a systematic study of the properties of pure hadronic compact stars.\nThe $\\beta$-equilibrated neutron star matter using this EoS with a thin crust\nis able to describe highly-massive compact stars, such as PSR B1516+02B with a\nmass M=1.94$^{+0.17}_{-0.19}$ M$_\\odot$ and PSR J0751+1807 with a mass\nM=2.1$\\pm$0.2 M$_\\odot$ to a 1$\\sigma$ confidence level.\n

The stability and other physical properties of a class of regular black holes, quasiblack holes, and other electrically charged compact objects are investigated in the present work. The compact objects are obtained by solving the Einstein-Maxwell system of equations assuming spherical symmetry in a static spacetime. The spacetime is split in two regions by a spherical surface of coordinate radius $a$. The interior region contains a nonisotropic charged fluid with a de Sitter type equation of state, $p_r = -\rho_m$, $p_r$ and $\rho_m$ being respectively the radial pressure and the energy density of the fluid. The charge distribution is chosen as a well behaved power-law function. The exterior region is the electrovacuum Reissner-Nordstr\"om metric, which is joined to the interior metric through a spherical thin shell (a thin matter layer) placed at the radius $a$. The matter of the shell is assumed to be a perfect fluid satisfying a linear barotropic equation of state, ${\cal P}=\omega\sigma$, with ${\cal P}$ and $\sigma$ being respectively the pressure and energy density of the shell, with $\omega$ being a constant. The exact solutions obtained are analyzed in some detail by exploring the interesting regions of parameter space, complementing the analysis of previous works on similar models. This is the first important contribution of the present study. The stability of the solutions are then investigated considering perturbations around the equilibrium position of the shell. This is the second and the most important contribution of this work. We find that there are stable objects in relatively large regions of the parameter space. In particular, there are stable regular black holes for all values of the parameter $\omega$ of interest. Other stable ultracompact objects as quasiblack holes, gravastars, and even overcharged stars are allowed in certain regions of the parameter space.

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.

Heavy baryons in compact stars

This work presents an algorithm for modeling a static spherically symmetric compact object satisfying the Eiesland condition (Eiesland in Am Math Soc 27:213, 1925), a necessary and sufficient condition that a general centro-symmetric space shall be of the class 1. The model parameters are obtained accordingly by employing the boundary conditions to the interior solutions. The equation of state has been extracted from the solution and one found that it is almost linear. These models are free of physical and geometric singularities and satisfy the necessary physical conditions to have astrophysical significance. The central and surface densities, and pressures of some compact stars like PSR J1614-2230, Vela X-1 have been calculated from these models. Detailed analyses of these models have also been made with the help of numerical and graphical studies.