Anisotropic strange star inspired by Finsler geometry

In this paper, we report on a study of the anisotropic strange stars under Finsler geometry. Keeping in mind that Finsler spacetime is not merely a generalization of Riemannian geometry rather the main idea is the projectivized tangent bundle of the manifold [Formula: see text], we have developed the respective field equations. Thereafter, we consider the strange quark distribution inside the stellar system followed by the MIT bag model equation-of-state (EoS). To find out the stability and also the physical acceptability of the stellar configuration, we perform in detail some basic physical tests of the proposed model. The results of the testing show that the system is consistent with the Tolman–Oppenheimer–Volkoff (TOV) equation, Herrera cracking concept, different energy conditions and adiabatic index. One important result that we observe is, the anisotropic stress reaches the maximum at the surface of the stellar configuration. We calculate (i) the maximum mass as well as the corresponding radius, (ii) the central density of the strange stars for finite values of bag constant [Formula: see text] and (iii) the fractional binding energy of the system. This study shows that Finsler geometry is especially suitable to explain massive stellar systems.

Modelling strains and stresses in continuously stratified rotating neutron stars

We introduce a Newtonian model for the deformations of a compressible, auto-gravitating and continuously stratified neutron star. The present framework can be applied to a number of astrophysical scenarios as it allows to account for a great variety of loading forces. In this first analysis, the model is used to study the impact of a frozen adiabatic index in the estimate of rotation-induced deformations: we assume a polytropic equation of state for the matter at equilibrium but, since chemical reactions may be slow, the perturbations with respect to the unstressed configuration are modeled by using a different adiabatic index. We quantify the impact of a departure of the adiabatic index from its equilibrium value on the stressed stellar configuration and we find that a small perturbation can cause large variations both in displacements and strains. As a first practical application, we estimate the strain developed between two large glitches in the Vela pulsar showing that, starting from an initial unstressed configuration, it is not possible to reach the breaking threshold of the crust, namely to trigger a starquake. In this sense, the hypothesis that starquakes could trigger the unpinning of superfluid vortices is challenged and, for the quake to be a possible trigger, the solid crust must never fully relax after a glitch, making the sequence of starquakes in a neutron star an history-dependent process.

The “Planckonions”

We consider a spherically symmetric stellar configuration with a density profile [Formula: see text]. This configuration satisfies the Schwarzchild black hole condition [Formula: see text] for every [Formula: see text]. We refer to it as “Planckonion”. The interesting thing about the Planckonion is that it has an onion-like structure. The central sphere with radius of the Planck-length [Formula: see text] has one unit of the Planck-mass [Formula: see text]. Subsequent spherical shells of radial width [Formula: see text] contain exactly one unit of [Formula: see text]. We study this stellar configuration using Tolman–Oppenheimer–Volkoff equation and show that the equation is satisfied if pressure [Formula: see text]. On the geometrical side, the space component of the metric blows up at every point. The time component of the metric is zero inside the star but only in the sense of a distribution (generalized function). The Planckonions mimic some features of black holes but avoid appearance of central singularity because of the violation of null energy conditions.

Relativistic anisotropic model of strange star SAX J1808.4-3658 admitting quadratic equation of state

In this paper, we study the behavior of static spherically symmetric relativistic model of the strange star SAX J1808.4-3658 by exploring a new exact solution for anisotropic matter distribution. We analyze the comprehensive structure of the space–time within the stellar configuration by using the Einstein field equations amalgamated with quadratic equation of state (EoS). Further, we compare solutions of quadratic EoS model with modified Bose–Einstein condensation EoS and linear EoS models which can be generated by a suitable choice of parameters in quadratic EoS model. Subsequently, we compare the properties of strange star SAX J1808.4-3658 for all the three EoS models with the help of graphical representations.

A pure geometric approach to stellar structure: Mass–radius relation

This paper represents the second step towards understanding stellar structure using pure geometric tools. It is an attempt to get a theoretical expression for a mass–radius relation. The stellar model used has been obtained as an analytic solution of the field equations of a pure geometric field theory. The method suggested to get this relation is very simple. It depends mainly on a set of differential equations implying the vanishing of all components of a geometric material-energy tensor on a boundary of stellar configuration. The theoretical relation obtained is a linear one [Formula: see text] with one free parameter [Formula: see text] Comparison with observation, using a sample of lower main-sequence stars, members of binary systems, is given. For the primary members [Formula: see text], we get [Formula: see text]. It is worthy of mention that the model obtained is a simple one. Rotation, magnetic field, etc. are not considered in the present treatment. So, the model is far from being complete. It is just a step to show that pure geometric consideration objects can be used to treat problems of stellar structure.

Dark energy stars: Stable configurations

In present paper a spherically symmetric stellar configuration has been analyzed by assuming the matter distribution of the stellar configuration is anisotropic in nature and compared with the realistic objects, namely, the low mass X-ray binaries and X-ray pulsars. The analytic solution has been obtained by utilizing the dark energy equation of state for the interior solution corresponding to the Schwarzschild exterior vacuum solution at the junction interface. Several physical properties, like energy conditions, stability, mass–radius ratio, and surface redshift, are described through mathematical calculations as well as graphical plots. It is found that obtained mass–radius ratios of the compact star candidates like 4U 1820–30, PSR J 1614–2230, Vela X-1, and Cen X-3 are very much consistent with the observed data by Gangopadhyay et al. (Mon. Not. R. Astron. Soc. 431, 3216 (2013)). So our proposed model would be useful in the investigation of the possible clustering of dark energy.

Radiating collapse in the presence of anisotropic stresses

In this paper, we investigate the effect of anisotropic stresses (radial and tangential pressures being unequal) for a collapsing fluid sphere dissipating energy in the form of radial flux. The collapse starts from an initial static sphere described by the Bowers and Liang solution and proceeds until the time of formation of the horizon. We find that the surface redshift increases as the stellar fluid moves away from isotropy. We explicitly show that the formation of the horizon is delayed in the presence of anisotropy. The evolution of the temperature profiles is investigated by employing a causal heat transport equation of the Maxwell–Cattaneo form. Both the Eckart and causal temperatures are enhanced by anisotropy at each interior point of the stellar configuration.

A GENERAL RELATIVISTIC MODEL FOR SAX J1808.4-3658

We discuss the physical applicability of a model for a class of compact stars, employing Vaidya–Tikekar12 geometry of space–time. It is shown that the model can generate an equation of state (EOS) very similar to the one obtained by earlier workers for SAX J1808.4-3658 (SAX in short), assumed to be a strange star. The stellar configuration, as described by the model, is shown to be stable under radial perturbations. This may explain why the star SAX is known to be very stable compared to other low mass binary X-ray emitters.