Anisotropic strange stars in Tolman–Kuchowicz spacetime

We attempt to study a singularity-free model for the spherically symmetric anisotropic strange stars under Einstein’s general theory of relativity by exploiting the Tolman–Kuchowicz (Tolman in Phys Rev 55:364, 1939; Kuchowicz in Acta Phys Pol 33:541, 1968) metric. Further, we have assumed that the cosmological constant \(\varLambda \) is a scalar variable dependent on the spatial coordinate r. To describe the strange star candidates we have considered that they are made of strange quark matter distribution, which is assumed to be governed by the MIT bag equation of state. To obtain unknown constants of the stellar system we match the interior Tolman–Kuchowicz metric to the exterior modified Schwarzschild metric with the cosmological constant, at the surface of the system. Following Deb et al. (Ann Phys 387:239, 2017) we have predicted the exact values of the radii for different strange star candidates based on the observed values of the masses of the stellar objects and the chosen parametric values of the \(\varLambda \) as well as the bag constant \({\mathcal {B}}\). The set of solutions satisfies all the physical requirements to represent strange stars. Interestingly, our study reveals that as the values of the \(\varLambda \) and \({\mathcal {B}}\) increase the anisotropic system become gradually smaller in size turning the whole system into a more compact ultra-dense stellar object.     

Anisotropic quark stars in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

The aim of this paper is to analyze the nature of anisotropic spherically symmetric relativistic star models in the framework of f(R, T) gravity. To discuss the features of compact stars, we consider that in the interior of the stellar system, the fluid distribution is influenced by MIT bag model equation of state. We construct the field equations by employing Krori–Barua solutions and obtain the values of unknown constants with the help of observational data of Her X-1, SAX J 1808.4-3658, RXJ 1856-37 and 4U1820-30 star models. For a viable f(R, T) model, we study the behavior of energy density, transverse as well as radial pressure and anisotropic factor in the interior of these stars for a specific value of the bag constant. We check the physical viability of our proposed model and stability of stellar structure through energy conditions, causality condition and adiabatic index. It is concluded that our model satisfies the stability criteria as well as other physical requirements, and the value of bag constant is in well agreement with the experimental value which highlights the viability of our considered model.     

All possible tripartitions of $${}^{}$$U isotope in collinear configuration

In this work we provide a framework for modelling compact stars in which the interior matter distribution obeys a generalised Chaplygin equation of state. The interior geometry of the stellar object is described by a spherically symmetric line element which is simultaneously co-moving and isotropic with the exterior space–time being vacuum. We are able to integrate the Einstein field equations and present closed form solutions which adequately describe compact strange star candidates such as 4U 1538-52, PSR J1614-2230, Vela X-1 and Cen X-3 (Gangopadhyay et al, Mon. Not. R. Astron. Soc. 431, 3216 (2013)).     

A family of charged compact objects with anisotropic pressure

Utilizing an ansatz developed by Maurya et al. we present a class of exact solutions of the Einstein–Maxwell field equations describing a spherically symmetric compact object. A detailed physical analysis of these solutions in terms of stability, compactness and regularity indicates that these solutions may be used to model strange star candidates. In particular, we model the strange star candidate Her X-1 and show that our solution conforms to observational data to an excellent degree of accuracy. An interesting and novel phenomenon which arises in this model is the fact that the relative difference between the electromagnetic force and the force due to the pressure anisotropy changing sign within the stellar interior. This may be an additional mechanism required for stability against cracking of the stellar object.     

New stiff matter solutions to Einstein equations

New exact solutions are presented to the Einstein field equations which are spherically symmetric and static, with a perfect fluid distribution of matter satisfying the equation of state=p. One of the obtained solutions may only be used locally, the other represents the stellar interior globally and is singularity-free.     

Strange stars in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) theories of gravity in the Palatini formalism

In the present work we study strange stars in f(R) theories of gravity in the Palatini formalism. We consider two concrete well-known cases, namely the \(R+R^2/(6 M^2)\) model as well as the \(R-\mu ^4/R\) model for two different values of the mass parameter M or \(\mu \). We integrate the modified Tolman–Oppenheimer–Volkoff equations numerically, and we show the mass-radius diagram for each model separately. The standard case corresponding to the General Relativity is also shown in the same figure for comparison. Our numerical results show that the interior solution can be vastly different depending on the model and/or the value of the parameter of each model. In addition, our findings imply that (i) for the cosmologically interesting values of the mass scales \(M,\mu \) the effect of modified gravity on strange stars is negligible, while (ii) for the values predicting an observable effect, the modified gravity models discussed here would be ruled out by their cosmological effects.     

Dense stars with exotic configurations

In this paper, we consider dense stars with configurations expected from the SU(3)_C×SU(2)_W× U(1) standard model of strong and electroweak interactions. Following a recent suggestion that strange matter, a form of (uds) quark matter, may be the true ground state of hadronic matter, we investigate the prospect for the existence of dense stars consisting partially, or entirely, of strange matter by comparing the relative stability between neutron matter and strange matter. It is found that the restriction on the maximum star mass holds in all cases, including a pure strange star, a pure neutron star, and a neutron star with a quark core. It is also found that the choice of both the bag constantB and the strong coupling constant _s has a decisive effect on the relative stability between strange matter and neutron matter. For currently accepted values of (B, _s), anA= dense starcannot consist entirely,nor partially, of strange matter. Nevertheless, such conclusion may be subject to change if corrections ofO ( _s ² ) or other effects are taken into account. Finally, we use the framework of Tolman, Oppenheimer, and Volkoff to analyze two cases of boson stars: gluon stars and stars consisting of massive scalar particles (massive bosons). It is found that, in the case of gluon stars, the presence of the bag constant in the QCD vacuum yields results very similar to that found in quark stars. On the other hand, soliton stars consisting of massive bosons exist if there is some background pressure which plays the role similar to the bag constant for lowering the matter pressure. The stability problem for both gluon stars and soliton stars is briefly discussed.     

A new model for spherically symmetric charged compact stars of embedding class 1

In the present study we search for a new stellar model with spherically symmetric matter and a charged distribution in a general relativistic framework. The model represents a compact star of embedding class 1. The solutions obtained here are general in nature, having the following two features: first of all, the metric becomes flat and also the expressions for the pressure, energy density, and electric charge become zero in all the cases if we consider the constant \(A=0\), which shows that our solutions represent the so-called ‘electromagnetic mass model’ [17], and, secondly, the metric function \(\nu (r)\), for the limit n tending to infinity, converts to \(\nu (r)=C{r}^{2}+ ln~B\), which is the same as considered by Maurya et al. [11]. We have investigated several physical aspects of the model and find that all the features are acceptable within the requirements of contemporary theoretical studies and observational evidence.     

An approximate global solution of Einstein’s equation for a rotating compact source with linear equation of state

We use analytic perturbation theory to present a new approximate metric for a rigidly rotating perfect fluid source with equation of state (EOS) $\epsilon +(1-n)p=\epsilon _0$ . This EOS includes the interesting cases of strange matter, constant density and the fluid of the Wahlquist metric. It is fully matched to its approximate asymptotically flat exterior using Lichnerowicz junction conditions and it is shown to be a totally general matching using Darmois–Israel conditions and properties of the harmonic coordinates. Then we analyse the Petrov type of the interior metric and show first that, in accordance with previous results, in the case corresponding to Wahlquist’s metric it can not be matched to the asymptotically flat exterior. Next, that this kind of interior can only be of Petrov types I, D or (in the static case) O and also that the non-static constant density case can only be of type I. Finally, we check that it can not be a source of Kerr’s metric.     

Gravitational Collapse of Null Strange Quark Fluid and Cosmic Censorship

We study the gravitational collapse of the general spherically symmetric null strange quark fluid having the equation of state, p = ( – 4B)/n, where B is the bag constant. It is an interesting feature that the initial data set giving rise to a naked singularity in the Vaidya collapse of null fluid gets covered due to the presence of the strange quark matter component. Its implication for the Cosmic Censorship Conjecture is discussed.     

Spherical Symmetric Perfect Fluid Collapse in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

This paper contains the study of spherically symmetric perfect fluid collapse in the frame work of f(R, T) modified theory of gravity. We proceed our work by considering the non-static spherically symmetric background in the interior and static spherically symmetric background in the exterior regions of the star. The junction conditions between exterior and interior regions are presented by matching the exterior and interior regions. The field equations are solved by taking the assumptions that the Ricci scalar as well as the trace of energy-momentum tensor are to be constant, for a particular f(R, T) model. By inserting the solution of the field equations in junction conditions, we evaluate the gravitational mass of the collapsing system. Also, we discuss the apparent horizons and their time formation for different possible cases. It is concluded that the term f(R ₀, T ₀) behaves as a source of repulsive force and that’s why it slowdowns the collapse of the matter.     

The Vlasov–Poisson System for Stellar Dynamics in Spaces of Constant Curvature

We obtain a natural extension of the Vlasov–Poisson system for stellar dynamics to spaces of constant Gaussian curvature \({\kappa \ne 0}\): the unit sphere \({\mathbb S^2}\), for \({\kappa > 0}\), and the unit hyperbolic sphere \({\mathbb H^2}\), for \({\kappa < 0}\). These equations can be easily generalized to higher dimensions. When the particles move on a geodesic, the system reduces to a 1-dimensional problem that is more singular than the classical analogue of the Vlasov–Poisson system. In the analysis of this reduced model, we study the well-posedness of the problem and derive Penrose-type conditions for linear stability around homogeneous solutions in the sense of Landau damping.     

An Analysis of Charged Anisotropic Star with de Sitter Spacetime

We propose a model for charged anisotropic star in de Sitter spacetime. We have taken Krori and Barua (J. Phys. A, Math. Gen. 8, 508, 1975) metric in de Sitter spacetime with non-zero cosmological constant. The model is free from singularity. We incorporate the existence of the cosmological constant on a small scale to study the structure of anisotropic charged star. To solve the Einstein-Maxwell field equations we assume the relation between the radial and transverse pressure as p _t ?p _r =g q(r)² r ² (where g is a non-zero positive constant). The physical conditions inside the stellar model are also discussed.     

模型参数对奇异星性质的影响

用有效质量口袋模型描述奇异夸克物质,研究了耦合常数和口袋常数的选取对奇异夸克物质的状态方程及奇异星性质的影响.结果表明,随着耦合常数和口袋常数的增大,奇异夸克物质的状态方程变软,相应的奇异星的引力质量和对应的半径均变小.当耦合常数从0.5增大到2.0时,奇异星的质量从1.43M_⊙(M_⊙=1.99×10³⁰ kg)减小到1.25M_⊙,相应的半径由8.3 km减小到7.7 km;当口袋常数B^1/4由160 MeV增大到175 MeV时,奇异星的质量和半径分别由1.47M_⊙和8.6 km减小到1.22M_⊙和7.4 km.这说明奇异夸克物质及奇异星的性质明显依赖于模型参数的取值. 关键词： 模型参数 奇异星 状态方程 质量-半径关系     

Anisotropic Strange Star in 5D Einstein-Gauss-Bonnet Gravity

In this paper, we investigated a new anisotropic solution for the strange star model in the context of 5D Einstein-Gauss-Bonnet (EGB) gravity. For this purpose, we used a linear equation of state (EOS), in particular pr=βρ+γ, (where β and γ are constants) together with a well-behaved ansatz for gravitational potential, corresponding to a radial component of spacetime. In this way, we found the other gravitational potential as well as main thermodynamical variables, such as pressures (both radial and tangential) with energy density. The constant parameters of the anisotropic solution were obtained by matching a well-known Boulware-Deser solution at the boundary. The physical viability of the strange star model was also tested in order to describe the realistic models. Moreover, we studied the hydrostatic equilibrium of the stellar system by using a modified TOV equation and the dynamical stability through the critical value of the radial adiabatic index. The mass-radius relationship was also established for determining the compactness and surface redshift of the model, which increases with the Gauss-Bonnet coupling constant α but does not cross the Buchdahal limit.     

Generalized isothermal models with strange equation of state

We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the electromagnetic field. New exact solutions are found to the Einstein-Maxwell system. A particular case is shown to be regular at the stellar centre. In the isotropic limit we regain the general relativistic isothermal Universe. We show that the mass corresponds to the values obtained previously for quark stars when anisotropy and charge are present.      

Wormholes, Classical Limit and Dynamical Vacuum in Quantum Cosmology

First a Friedmann-Robertson-Walker (FRW)universe filled with dust and a conformally invariantscalar field is quantized. For the closed model we finda discrete set of wormhole quantum states. In the case of flat spacelike sections we find states withclassical behaviour at small values of the scale factorand quantum behaviour for large values of the scalefactor. Next we study a FRW model with a conformally invariant scalar field and a nonvanishingcosmological constant dynamically introduced byregarding the vacuum as a perfect fluid with equation ofstate p = –. The ensuing Wheeler-DeWittequation turns out to be a bona fide Schrodinger equation, andwe find that there are realizable states with a definitevalue of the cosmological constant. Once again we findfinite-norm solutions to the Wheeler-DeWitt equation with definite values of thecosmological constant that represent wormholes,suggesting that in quantum cosmological models with asimple matter content wormhole states are a commonoccurrence.     

Topological Spin Excitations Induced by an External Magnetic Field Coupled to a Surface with Rotational Symmetry

We study the Heisenberg model in an external magnetic field on curved surfaces with rotational symmetry. The Euler–Lagrange static equations, derived from the Hamiltonian, lead to the inhomogeneous double sine-Gordon equation. Nonetheless, if the magnetic field is coupled to the metric elements of the surface, and consequently to its curvature, the homogeneous double sine-Gordon equation emerges and a $2\pi $ -soliton solution is obtained. In order to satisfy the self-dual equations, surface deformations are predicted to appear at the sector where the spin direction is opposite to the magnetic field. On the basis of the model, we find the characteristic length of the $2\pi $ -soliton for three specific rotationally symmetric surfaces: the cylinder, the catenoid, and the hyperboloid. On finite surfaces, such as the sphere, torus, and barrels, fractional $2\pi $ -solitons are predicted to appear.     

Reconstructions of the dark-energy equation of state and the inflationary potential

We use a mathematical approach based on the constraints systems in order to reconstruct the equation of state and the inflationary potential for the inflaton field from the observed spectral indices for the density perturbations \(n_{s}\) and the tensor to scalar ratio r. From the astronomical data, we can observe that the measured values of these two indices lie on a two-dimensional surface. We express these indices in terms of the Hubble slow-roll parameters and we assume that \(n_{s}-1=h\left( r\right) \). For the function \(h\left( r\right) \), we consider three cases, where \(h\left( r\right) \) is constant, linear and quadratic, respectively. From this, we derive second-order equations whose solutions provide us with the explicit forms for the expansion scale-factor, the scalar-field potential, and the effective equation of state for the scalar field. Finally, we show that for there exist mappings which transform one cosmological solution to another and allow new solutions to be generated from existing ones.     

Self-Similar Solutions for a Fractional Thin Film Equation Governing Hydraulic Fractures

In this paper, self-similar solutions for a fractional thin film equation governing hydraulic fractures are constructed. One of the boundary conditions, which accounts for the energy required to break the rock, involves the toughness coefficient K ≥ 0. Mathematically, this condition plays the same role as the contact angle condition in the thin film equation. We consider two situations: The zero toughness (K = 0) and the finite toughness K ∈ (0, ∞) cases. In the first case, we prove the existence of self-similar solutions with constant mass. In the second case, we prove that for all K > 0 there exists an injection rate for the fluid such that self-similar solutions exist.