Narrow Results

Using modified $f(T)$ gravity and the diagonal tetrad, we propose a new kind of analytical solution to describe anisotropic charged stellar structures in this study. We obtain precise solutions by applying the linear form of $f(T)$ as $f(T)=\gamma T+\delta$ in the framework of Tolman–Kuchowicz physically sound metric potentials. The stellar structures of the compact star EXO 1785-248 are then investigated using the model by incorporating a linear equation of state relating the radial pressure $p_r$ and the matter density $\rho$. We computed the closed-form expressions for the model parameters and illustrated their characteristics. The comprehensive graphical analysis demonstrates the scientific plausibility, causality, and dynamical stability of the model describing charged anisotropic stars. Finally, using the M-R curve, we estimate the numerical values of mass for different values of $\gamma$. The observational data of the neutron star candidates 4U 1820-30, PSR J1614-2230, and PSR J2215 + 5135 are covered by the maximum allowable masses for different values of $\gamma$ additionally, when $\gamma =2.5$, the charged compact star’s maximum permissible mass is calculated to be $2.56M_{\odot }$, which could indicate the secondary component of the GW190814 event discovered by LIGO/VIRGO experiments.

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 $\alpha$. 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 $\alpha$ on the physical parameters are depicted graphically and numerically.

This work aims to investigate the self-bound anisotropic solution for spherical objects within the $f({𝒬})$ gravity, where $Q$ is called a nonmetric scalar. Initially, the equation of motion for gravity theory is obtained by using a linear representation of the function $f({𝒬})$ as $f({𝒬})={𝜖}_{1}Q+{𝜖}_2$, here parameters ${𝜖}_1$ and ${𝜖}_2$ are used. Subsequently, the acquired system of differential equations was solved by including a radial metric component in conjunction with the specific ansatz of the anisotropy factor. The values of the constants required for the solution were established by using the Schwarzschild (Anti-) de Sitter exterior solution. In order to assess the physical acceptability of a solution, it is necessary to examine several physical conditions, including the behavior of pressure, density, adiabatic index, and equilibrium conditions, for different values of the parameter ‘${𝜖}_1$’ inside the star system. These requirements are visually represented by graphical analysis. The current solution meets all the physical requirements, indicating that it is a suitable model of a compact stellar structure.

We investigate whether compact stars having Tolman-like interior geometry admit conformal symmetry. Taking anisotropic pressure along the two principal directions within the compact object, we obtain physically relevant quantities such as transverse and radial pressure, density and redshift function. We study the equation of state (EOS) for the matter distribution inside the star. From the relation between pressure and density function of the constituent matter, we explore the nature and properties of the interior matter. The redshift function and compactness parameter are found to be physically reasonable. The matter inside the star satisfies the null, weak and strong energy conditions. Finally, we compare the masses and radii predicted from the model with corresponding values in some observed stars.

Recently, Hod showed that neutral stationary scalar field clouds can exist outside neutral reflecting compact stars. In the present paper, we extend the discussion by considering charged stationary scalar fields in the background of charged reflecting compact stars. If stationary scalar clouds exist, we analytically show that the field frequency belongs to an interval. For certain discrete field frequency values in the interval, we obtain numerical solutions of scalar field clouds. We also study effects of model parameters on discrete frequency.

A class of solutions of Einstein field equations satisfying Karmarkar embedding condition is presented which could describe static, spherical fluid configurations, and could serve as models for compact stars. The fluid under consideration has unequal principal stresses i.e. fluid is locally anisotropic. A certain physically motivated geometry of metric potential has been chosen and codependency of the metric potentials outlines the formation of the model. The exterior spacetime is assumed as described by the exterior Schwarzschild solution. The smooth matching of the interior to the exterior Schwarzschild spacetime metric across the boundary and the condition that radial pressure is zero across the boundary lead us to determine the model parameters. Physical requirements and stability analysis of the model demanded for a physically realistic star are satisfied. The developed model has been investigated graphically by exploring data from some of the known compact objects. The mass-radius (M-R) relationship that shows the maximum mass admissible for observed pulsars for a given surface density has also been investigated. Moreover, the physical profile of the moment of inertia (I) thus obtained from the solutions is confirmed by the Bejger–Haensel concept.

For the first time, we present Einstein’s cluster model in embedding class one spacetime. This paper shows that for any neutral configurations there is only one Einstein cluster solution in embedding class one. In fact, one can find two solutions where the first solution i.e. $g_{rr}=e^{\lambda }=1$ and $g_{tt}=e^{\nu }=C$ is an unphysical one as it has zero density profile as well as violates the Pandey–Sharma condition (i.e. not a class one solution). However, the second solution can describe matter distribution representing Einstein’s cluster which is in static and equilibrium as it satisfies the static stability criterion and TOV-equation. The second solution not only satisfies the above conditions, but also satisfies the energy conditions. The equation of state parameter ${\omega }_t$ is less than unity signifying that it can represent physical matters. Further, we have also shown that the Einstein’s clusters may also exhibit the properties of compact stars.

In this paper, we review how the “cusp” predicted in the nuclear symmetry energy generated by a topology change at density $n_{1/2}\gtrsim 2n_0$ can have a surprising consequence, so far unrecognized in nuclear physics and astrophysics communities, on the structure of dense compact-star matter. The topology change translated into nuclear EFT with “effective” QCD degrees of freedom encoded in hidden local and scale symmetries predicts an EoS that is soft below and stiff above$n\gtrsim n_{1/2}$, and yields the properties of neutron stars with no tension with all the astrophysical observations available up to date. Furthermore it describes the interior core of the massive stars populated by fractionally charged quasi-fermions that are neither baryonic nor quarkonic. It is argued that the cusp “buried” in the symmetry energy resulting from strong correlations with hidden heavy degrees of freedom leads, at $n\gtrsim n_{1/2}$, to a “pseudo-conformal” sound speed, $v_{\mathrm{\text{pcs}}}^2/c^2\approx 1/3$, converged from below at $n_{1/2}$. It is not conformal since the trace of energy–momentum tensor is not zero even in the chiral limit. It reflects an emergent scale symmetry. This observation with the topology change implies that the quantities accurately measured at $\sim n_0$ cannot give a qualitatively stringent constraint for what takes place at the core density of compact stars $\sim (3\text{–}7)n_0$. This is because there intervenes a change of degrees of freedom in the effective field theory. We discuss the implication of this on the recent PREX-II “dilemma” in the measured skin thickness of ${}^{208}\mathrm{\text{Pb}}$.

This paper explores a new embedding anisotropic charged version of a solution to Einstein–Maxwell field equations in four-dimensional spacetime through the Karmarkar conditions and the gravitational decoupling via minimal geometric decoupling (MGD) technique by choosing Pant’s interior solution [Astrophys. Space Sci. 331, 633 (2011)] as a seed solution to coupled system. Later, we integrate the coupled system within the MGD and explore a family of solutions to represent the realistic structure of nonrotating compact objects. Through the matching of the interior solutions so obtained to the exterior Reissner–Nordström metric, we tune the arbitrary constants for feasible models. After that, we subject our model to a rigorous test for a chosen parameter space to verify the physical viability of the solution for the neutron stars in EXO 1785-248 for a range of values of the decoupling constant $\sigma$. Further, we prove that the constant $\sigma$ is inherently connected to critical physical properties such as the gravitational and surface redshifts, compactification factor, mass/radius relation, etc., of the same compact star candidate EXO 1785-248. The solutions thus obtained exhibit physically viable features which are thoroughly demonstrated through graphical plots.

In recent years, a class of compact objects called gravastars have drawn immense interest as regular solutions to end state stellar collapse. Since the energy density involved in collapse process is expected to be high, it is a natural choice to study such compact objects in context of modified gravity theories which reduce to General Relativity (GR) in the low energy regime. We have already framed a model of gravastar in such a modified gravity framework involving extra dimensional Randall–Sundrum (RS) single brane gravity [R. Sengupta, S. Ghosh, S. Ray, B. Mishra and S. K. Tripathy, Phys. Rev. D 102, 024037 (2020)]. As a sequel in this paper, we substantially improve our previous model by choosing the Kuchowicz function as one of the metric potentials, which leads to many new interesting results and physical features from our analysis as discussed in this paper. Also, we provide essential additional stability checks on our gravastar model to investigate the possibility of any instability creeping in due to the higher-dimensional framework. Our present improved gravastar model is found to clear all the stability checks successfully. Very interestingly, the static spherically symmetric matter distributions are found to accommodate both classes of solutions obeying and violating the modified energy conditions on the RS brane as we find in this work. We can conclude from our analysis that the Kuchowicz metric potential is very effective for describing regular solutions to compact objects at substantially high energies on the three-brane.

In this study, we investigated an interior solution of a static spherically symmetric dark energy star model incorporating anisotropic fluid and a state parameter of the type cosmological constant, achieved through parametrization of the Finch and Skea metric function. The motivation for this study stems from the lack of investigation of dark energy star models in relation to BHs in the previous studies, and from recent proposals suggesting that dark energy might originate inside BHs. This opens up the opportunity to explore the dark energy star model and establish its relationship with BHs. The structural profiles of the models, including mass function, energy density, compactness, surface redshift, and local acceleration due to gravity, were investigated. Analysis involving the matching of the exterior Schwarzschild vacuum solution to the interior spacetime at a junction interface was also explored. The results demonstrate that this solution is free of singularities, possessing outward gravitational repulsion with an infinite property near the surface boundary. Notably, the model exhibited an infinite redshift surface, and a compactness of one half, thus evading the Buchdahl limit. It fulfills the energy conditions except for the strong energy conditions and remains in a state of static equilibrium, upheld by both hydro-static and anisotropic forces. Numerical values of physical properties for various types of astrophysical BH candidates have been determined. Overall, the obtained model is physically unique and represents the most compact and extreme model of dark energy stars. Some features of this model resemble those of BHs, rendering it indistinguishable from BHs.

Geometrization of the fundamental interactions has been extensively studied during the century. The idea of introducing compactified spatial dimensions originated by Kaluza and Klein. Following their approach, several model were built representing quantum numbers (e.g. charges) as compactified space-time dimensions. Such geometrized theoretical descriptions of the fundamental interactions might lead us to get closer to the unification of the principle theories. Here, we apply a $3+1_C+1$ dimensional theory, which contains one extra compactified spatial dimension $1_C$ in connection with the flavor quantum number in Quantum Chromodynamics. Within our model the size of the $1_C$ dimension is proportional to the inverse mass-difference of the first low-mass baryon states. We used this phenomena to apply in a compact star model — a natural laboratory for testing the theory of strong interaction and the gravitational theory in parallel. Our aim is to test the modification of the measurable macroscopical parameters of a compact Kaluza–Klein star by varying the size of the compactified extra dimension. Since larger the $R_C$ the smaller the mass difference between the first spokes of the Kaluza–Klein ladder resulting smaller-mass stars. Using the Tolman–Oppenheimer–Volkov equation, we investigate the $M$-$R$ diagram and the dependence of the maximum mass of compact stars. Besides testing the validity of our model we compare our results to the existing observational data of pulsar properties for constraints.

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.

Effect of maximum amount of charge a compact star can hold, is studied here. We analyze the different features in the renewed stellar structure and discuss the reasons why such huge charge is possible inside a compact star. We studied a particular case of a polytropic equation of state (EOS) assuming the charge density is proportional to the mass density. Although the global balance of force allows a huge charge, the electric repulsion faced by each charged particle forces it to leave the star, resulting in the secondary collapse of the system to form a charged black hole.

P-Stars are a new class of compact stars made of up and down quarks in β-equilibrium with electrons in an Abelian chromomagnetic condensate. We show that P-Stars are able to account for compact stars with R≲6 Km, as well as stars with radius comparable with canonical Neutron Stars. We find that cooling curves of P-Stars compare rather well with observational data. We suggest that P-Matter produced at the primordial deconfinement transition is a viable candidate for baryonic Cold Dark Matter. Finally, we show that P-Stars are able to overcome the gravitational collapse even for masses much greater than 10⁶ M_⊙.

We calculate the maximum mass of the class of compact stars described by the Vaidya–Tikekar²⁷ model. The model permits a simple method of systematically fixing bounds on the maximum possible mass of cold compact stars with a given value of radius or central density or surface density. The relevant equations of state are also determined. Although simple, the model is capable of describing the general features of the recently observed very compact stars. For the calculation, no prior knowledge of the equation of state (EOS) is required. This is in contrast to earlier calculations for maximum mass which were done by choosing first the relevant EOSs and using those to solve the TOV equation with appropriate boundary conditions. The bounds obtained by us are comparable and, in some cases, more restrictive than the earlier results.

In this paper we study the isotropic cases of static charged fluid spheres in general relativity. For this purpose we consider two different specializations and under these we solve the Einstein–Maxwell field equations in isotropic coordinates. The analytical solutions thus obtained are matched to the exterior Reissner–Nordström solutions which concern the values for the metric coefficients e^ν and e^μ. We derive the pressure, density and pressure-to-density ratio at the center of the charged fluid sphere and boundary R of the star. Our conclusion is that static charged fluid spheres provide a good connection to compact stars.

Recently, the small value of the cosmological constant and its ability to accelerate the expansion of the universe is of great interest. We discuss the possibility of forming of anisotropic compact stars from this cosmological constant as one of the competent candidates of dark energy. For this purpose, we consider the analytical solution of Krori and Barua metric. We take the radial dependence of cosmological constant and check all the regularity conditions, TOV equations, stability and surface redshift of the compact stars. It has been shown as conclusion that this model is valid for any compact star and we have cited 4U 1820-30 as a specific example of that kind of star.

A class of solutions describing the interior of a static spherically symmetric compact anisotropic star is reported. The analytic solution has been obtained by utilizing the Finch and Skea [Class. Quantum Grav.6 (1989) 467] ansatz for the metric potential g_rr which has a clear geometric interpretation for the associated background spacetime. Based on physical grounds, appropriate bounds on the model parameters have been obtained and it has been shown that the model admits an equation of state (EOS) which is quadratic in nature.

In this paper, we are willing to develop a model of an anisotropic star by choosing a new $g_{rr}$ metric potential. All the physical parameters like the matter density, radial and transverse pressure are regular inside the anisotropic star, with the speed of sound less than the speed of light. So the new solution obtained by us gives satisfactory description of realistic astrophysical compact stars. The model of this paper is compatible with observational data of compact objects like RX J1856-37, Her X-1, Vela X-12 and Cen X-3. A particular model of Her X-1 (Mass 0.98 $M_{\odot }$ and radius=6.7 km.) is studied in detail and found that it satisfies all the condition needed for physically acceptable model. Our model is described analytically as well as with the help of graphical representation.