A New Charged Anisotropic Compact Star Model in General Relativity

Relativistic models for anisotropic compact stars: A review

In the present article, we have constructed a static charged anisotropic compact star model of Einstein field equations for a spherically symmetric space-time geometry. Specifically, we have extended the charged isotropic Heintzmann solution to an anisotropic domain. To address this work, we have employed the gravitational decoupling through the so called minimal geometric deformation approach. The charged anisotropic model is representing the realistic compact objects such as RXJ1856-37 and SAX J1808.4-3658(SS2). We have reported our results in details for the compact star RXJ1856-37 on the ground of physical properties such as pressure, density, velocity of sound, energy conditions, stability conditions, Tolman–Oppenheimer–Volkoff equation and redshift etc.

This article investigates the physical properties and stability of an isotropic compact star in F(Q,T) gravity, where T denotes the trace of the energy-momentum tensor and Q represents the nonmetricity scalar. In the present study, the impact of F(Q,T) gravity on the stability and structure of compact stars is investigated, considering a perfect fluid distribution and adopting the functional form F(Q,T)=ξ1Q+ξ2T. The field equations are solved using the two-step method proposed by Gupta and Jasim [Astrophys. Space Sci. 283 (2003) 337], along with the Buchdahl ansatz given by eφ=ϒ(1+ϵr2)ϒ+ϵr2. To investigate the physical properties of the LMC X-4 compact star, a static spherically symmetric metric is employed in the interior region, while a Reissner-Nordstrom exterior metric is adopted for the exterior region. In the interior region of the proposed stellar object, we analyze the behaviour of the spacetime metric functions (eφ and eϑ), energy density (ρ), pressure (P), charge (q), ratio of pressure to density (Ω) and the energy conditions. The equilibrium state of the star is analysed using the Tolman-Oppenheimer-Volkoff (TOV) equation, expressed as FG+FH+F(Q,T)+FQ=0. To assess the stability of the configuration, we examine the adiabatic index (Γ), the causality condition, regularity conditions, the well-behaved condition and the stability against convection criterion.

New exact models of ideal gas in 5D EGB using curvature coordinates

Solving Tolman-Oppenheimer-Volkoff Equations in F(T) Gravity: A Novel Approach Applied to Polytropic Equations of State

In this article, we have presented a completely new, well-behaved, physically acceptable and stable anisotropic fluid sphere model. For this purpose we have used a well-known Vaidya-Tikekar [J. Astrophys. Astron. 3, 325 (1982)] ansatz for metric potential ${g}_{rr}$ to generate the model. We have investigated the various physical aspects for our model such as energy density, pressure (radial as well as transverse), anisotropy factor, mass, compactness parameter, surface, and gravitational redshifts. Energy conditions, equilibrium, and stability analysis has been done using graphs. This ensured that our proposed solutions are well-behaved and hence represent physically acceptable models for anisotropic fluid spheres. For comparison with observational data we have considered the compact stars: Her X-1, $4\mathrm{U}1538\penalty1000-\hskip0pt52$, SAX $\mathrm{J}1808.4\penalty1000-\hskip0pt3658$, LMC X-4, SMC X-1, EXO $1785\penalty1000-\hskip0pt248$, Cen X-3, 4U $1820\penalty1000-\hskip0pt30$, PSR $\mathrm{J}1903+327$, 4U $1608\penalty1000-\hskip0pt52$, Vela X-1, PSR $\mathrm{J}1614\penalty1000-\hskip0pt2230$, Cyg X-2 and PSR $\mathrm{B}1913+16$. The calculated value of central density of each of these compact stars, using this model, is of order ${10}^{14}$ or ${10}^{15}$, which is considerably high and consistent with ultracompact stars. We have also estimated the approximate moment of inertia for each of the considered compact stars.

The main focus of this paper is to explore the possibility of providing a new family of exact solutions for suitable anisotropic spherically symmetric systems in the realm of general relativity involving the embedding spherically symmetric static metric into the five-dimensional pseudo-Euclidean space. In this regard, we ansatz a new metric potential lambda (r), and we obtained the other metric potential nu (r) by mains of embedding class one approach. The unknown constants are determined by the matching of interior space-time with the Schwarzschild exterior space-time. The physical acceptability of the generating celestial model for anisotropic compact stars is approved via acting several physical tests of the main salient features viz., energy density, radial and tangential pressures, anisotropy effect, dynamical equilibrium, energy conditions, and dynamical stability, which are well-compared with experimental statistics of four different compact stars: PSR J1416-2230, PSR J1903+327, 4U 1820-30 and Cen X-3. Conclusively, all the compact stars under observations are realistic, stable, and are free from any physical or geometrical singularities. We find that the embedding class one solution for anisotropic compact stars is viable and stable, plus, it provides circumstantial evidence in favor of super-massive pulsars.

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.

In the framework of Einstein’s theory of general relativity we present a new interior solution with a perfect fluid; this is constructed from the proposal of a gravitational redshift factor. The geometry is regular and density and pressure are monotonic decreasing functions; furthermore, the sound speed is smaller than the light speed and monotonic increasing. The solution depends on a parameter w ∈ (0, 2.037 550 932 5] related to the compactness of the star u = GM/c2R, the maximum value of which is u = 0.266 085 831 6, which allows for describing compact stars like quark stars or neutron stars. Although there is a diversity of stars for which the model can be used, we only apply this solution to describe the interior of a neutron star PSR J0348+0432. According to the observations, it is known that its mass M = (2.01 ± 0.04)M⊙ and its radius is between 12 062 and 12 957 km, so the value of the compactness is in the range u ∈ [0.224 484 5, 0.250 933 8]. In addition to the decreasing behavior of the mentioned pressure and density functions, the results are consistent with the density value range typical of neutron stars and the maximal central density of the star result to be 1.283 818 × 1018 kg/m3.

The physical metric in general relativity has been introduced by the author as the exact solution of Einstein equation that fits the observation of time delay of the solar system. The necessary and sufficient condition for the physical metric is that the speed of light on the angular direction is unchanged from that of vacuum. A striking result is that the radius size of a black hole and a neutron star (summarized as compact object hereafter) is found to be 2.60 times greater than predicted by the Schwarzschild metric. In this article, the gravitational lensing of the compact object at long distance is absent. In other words, it is a feature result of the physical metric that the effect of the gravitational lensing for compact object by itself disappears at long distance. It will be shown that the recent observations are consistent with the prediction of the physical metric.

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.

The strong gravitational potential of neutron stars (NSs) makes them ideal astrophysical objects for testing extreme gravity phenomena. We explore the potential of NS X-ray pulsed light curve observations to probe deviations from general relativity (GR) within the scalar–tensor theory (STT) of gravity framework. We compute the flux from a single, circular, finite-size hot spot, accounting for light bending, Shapiro time delay, and Doppler effect. We focus on the high-compactness regime, i.e., close to the critical GR value GM/(c2R)=0.284, over which multiple images of the spot appear and impact crucially the light curves. Our investigation is motivated by the increased sensitivity of the pulse to the scalar charge of the spacetime in such high compactness regimes, making these systems exceptionally suitable for scrutinizing deviations from GR, notably phenomena such as spontaneous scalarization, as predicted by STT. We find significant differences in NS observables, e.g., the flux of a single spot can differ up to 80% with respect to GR. Additionally, reasonable choices for the STT parameters that satisfy astrophysical constraints lead to changes in the NS radius relative to GR of up to approximately 10%. Consequently, scalar parameters might be better constrained when uncertainties in NS radii decrease, where this could occur with the advent of next-generation gravitational wave detectors, such as the Einstein Telescope and LISA, as well as future electromagnetic missions like eXTP and ATHENA. Thus, our findings suggest that accurate X-ray data of the NS surface emission, jointly with refined theoretical models, could constrain STTs.

We present a well behaved class of charged analogue of M.C. Durgapal (J. Phys. A, Math. Gen. 15:2637, 1982) solution. This solution describes charged fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. This solution gives us wide range of parameter for every positive value of n for which the solution is well behaved hence, suitable for modeling of super dense stars. Keeping in view of well behaved nature of this solution, one new class of solution is being studied extensively. Moreover, this class of solution gives us wide range of constant K (0≤K≤2.2) for which the solution is well behaved hence, suitable for modeling of super dense stars like strange quark stars, neutron stars and pulsars. For this class of solution the mass of a star is maximized with all degree of suitability, compatible with quark stars, neutron stars and pulsars. By assuming the surface density ρb=2×1014 g/cm3 (like, Brecher and Capocaso, Nature 259:377, 1976), corresponding to K=0 with X=0..235, the resulting well behaved model has the mass M=4.03MΘ, radius rb=19.53 km and moment of inertia I=1.213×1046 g cm2; for K=1.5 with X=0.235, the resulting well behaved model has the mass M=4.43MΘ, radius rb=18.04 km and moment of inertia I=1.136×1046 g cm2; for K=2.2 with X=0.235, the resulting well behaved model has the mass M=4.56MΘ, radius rb=17.30 km and moment of inertia I=1.076×1046 g cm2. These values of masses and moment of inertia are found to be consistent with the crab pulsars.

We study the nature of phase transitions between gaseous and condensed states in the self-gravitating Fermi gas at finite temperature in general relativity. The condensed states can represent compact objects such as white dwarfs, neutron stars, or dark matter fermion balls. The caloric curves depend on two parameters: the system size R and the particle number N. When N < NOV, where NOV is the Oppenheimer–Volkoff limit, there exists an equilibrium state for any value of the temperature T and energy E as in the nonrelativistic case [P.H. Chavanis, Int. J. Mod. Phys. B 20, 3113 (2006)]. Gravitational collapse is prevented by quantum mechanics (Pauli’s exclusion principle). When N > NOV, there is no equilibrium state below a critical energy and below a critical temperature. In that case, the system is expected to collapse toward a black hole. We plot the caloric curves of the general relativistic Fermi gas, study the different types of phase transitions that occur in the system, and determine the phase diagram in the (R, N) plane. The nonrelativistic results are recovered for N ≪ NOV and R ≫ ROV with NR3 fixed. The classical (non quantum) results are recovered for N ≫ NOV and R ≫ ROV with N∕R fixed. We discuss the commutation of the limits c → +∞ and ℏ → 0. We study the relativistic corrections to the nonrelativistic caloric curves and the quantum corrections to the classical caloric curves. We highlight a situation of physical interest where a self-gravitating Fermi gas, by cooling, first undergoes a phase transition toward a compact object (white dwarf, neutron star, dark matter fermion ball), then collapses into a black hole. This situation occurs in the microcanonical ensemble when NOV < N < 3.73 NOV. We also relate the phase transitions from a gaseous state to a core-halo state in the microcanonical ensemble to the onset of red-giant structure and to the supernova phenomenon.

Comparative analysis of Einstein gravity and Rastall gravity for the compact objects