Properties Of Stellar Objects Research Articles

Compact stellar structures in Weyl geometric gravity

We consider the structure and physical properties of specific classes of neutron, quark, and Bose-Einstein condensate stars in the conformally invariant Weyl geometric gravity theory. The basic theory is derived from the simplest conformally invariant action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and a matter term, respectively. The action is linearized in the Weyl scalar by introducing an auxiliary scalar field. To keep the theory conformally invariant the trace condition is imposed on the matter energy-momentum tensor. The field equations are derived by varying the action with respect to the metric tensor, Weyl vector field and scalar field. By adopting a static spherically symmetric interior geometry, we obtain the field equations, describing the structure and properties of stellar objects in Weyl geometric gravity. The solutions of the field equations are obtained numerically, for different equations of state of the neutron and quark matter. More specifically, constant density stellar models, and models described by the stiff fluid, radiation fluid, quark bag model, and Bose-Einstein condensate equations of state are explicitly constructed numerically in both general relativity and Weyl geometric gravity, thus allowing an in depth comparison between the predictions of these two gravitational theories. As a general result it turns out that for all the considered equations of state, Weyl geometric gravity stars are more massive than their general relativistic counterparts. As a possible astrophysical application of the obtained results we suggest that the recently observed neutron stars, with masses in the range of $2{M}_{\ensuremath{\bigodot}}$ and $3{M}_{\ensuremath{\bigodot}}$, respectively, could be in fact conformally invariant Weyl geometric neutron or quark stars.

Embedding class one solutions of anisotropic fluid spheres in modified $$f({\mathcal {G}})$$ gravity

The main purpose of current analysis is to study three different compact spheres LMC X-4, Cen X-3, and EXO 1785-248 in modified $$f({\mathcal {G}})$$ gravity. In this context, the well-known Karmarkar condition is used to choose the suitable metric coefficients. The Schwarzschild interior solution is used to determine the matching conditions, and all the unknown coefficients in metric potentials are calculated through matching conditions for different values of the model parameter K. The necessary properties of stellar objects are discussed in this study, and a detailed graphical analysis is provided to check the physical viability. The validity of obtained anisotropic solutions confirms that the results are physically well fitted with observed data and free from any singularity.

Anisotropic compact stars in the Buchdahl model: A comprehensive study

In this article, we present a class of relativistic solutions describing spherically symmetric and static anisotropic stars in hydrostatic equilibrium. For this purpose, we consider a particularized matric potential, namely, Buchdahl ansatz [Phys. Rev. D \textbf{116}, 1027 (1959).] which encompasses almost all the known analytic solutions to the spherically symmetric, static Einstein field equations(EFEs) with a perfect fluid source, including in particular the Vaidya-Tikekar and Finch-Skea. We here developed the model by considering an anisotropic spherically symmetric static general relativistic configuration that plays a significant effect on the structure and properties of stellar objects. We have considered eight different cases for generalized Buchdahl dimensionless parameter $K$, and analyzed them in a uniform manner. As a result, it turns out that all the considered cases are valid at every point in the interior spacetime. In addition to this, we show that the model satisfies all the energy conditions and maintains the hydrostatic equilibrium equation. In the framework of the anisotropic hypothesis, we consider analogue objects with similar mass and radii such as LMC X-4, SMC X-1, EXO 1785-248 \emph{etc} to restrict the model parameter arbitrariness. Also, establishing a relation between pressure and density in the form of $P = P (\rho)$, we demonstrate that EoSs can be approximated to a linear function of density. Despite the simplicity of this model, the obtained results are satisfactory.

Thermal properties of bodies in fractal and cantorian physics

Abstract Fundamental laws describing the heat diffusion in fractal environment are discussed. It is shown that for the three-dimensional space the heat radiation process occur in structures with fractal dimension D ∈ 〈0,1), whereas in structures with D ∈ (1,3〉 heat conduction and convection have the upper hand (generally in the real gases). To describe the heat diffusion a new law has been formulated. Its validity is more general than the Plank’s radiation law based on the quantum heat diffusion theory. The energy density w = f ( K , D ), where K is the fractal measure and D is the fractal dimension exhibit typical dependency peaking with agreement with Planck’s radiation law and with the experimental data for the absolutely black body in the energy interval kT Kℏc . The positions of the energy density maximums (for fractal dimensions D m W - Function u ( A ) = A + W [− A exp(− A )], where A ≈ 1.9510 and u = hc / λ m kT m ≈ 1.5275. The agreement of the fractal model with the experimental outcomes is documented for the spectral characteristics of the Sun. The properties of stellar objects (black holes, relict radiation, etc.) and the elementary particles fields and interactions between them (quarks, leptons, mesons, baryons, bosons and their coupling constants) will be discussed with the help of the described mathematic apparatus in our further contributions. The general gas law for real gases in its more applicable form than the widely used laws (e.g. van der Waals, Berthelot, Kammerlingh–Onnes) has been also formulated. The energy density, which is in this case represented by the gas pressure p = f ( K , D ), can gain generally complex value and represents the behaviour of real (cohesive) gas in interval D ∈ (1,3〉. The gas behaves as the ideal one only for particular values of the fractal dimensions (the energy density is real-valued). Again, it is shown that above the critical temperature ( kT > Kℏc ) and for fractal dimension D m > 2.0269 the results are comparable to the kinetics theory of real (ideal) gas (van der Waals equation of state, compressibility factor, Boyle’s temperature). For the critical temperature ( Kℏc = kT r ) the compressibility factor gains Z = 1 (except for the ideal gas case D = 3) also for the fractal dimension D = 1/ ϕ = 1.618033989, where ϕ is the golden mean value of the El Naschie’s golden mean field theory. To determine the minimum it is also possible to employ the Lambert’s W − Function u ( A ) = A + W [− A exp(− A )], where A ≈ 0.6779 and u ≈ −0.7330. The thermal properties of fractal structures (thermal capacity, thermal conductivity, diffusivity) and additional parameters (enthalpy, entropy, etc.) will be defined using the mathematic apparatus in the future. Good agreement of the fractal model with experimental data is documented on the compressibility factor of various gases.

Anisotropic Stars: Exact Solutions

We study the effects of anisotropic pressure on the properties of spherically symmetric, gravitationally bound objects. We consider the full general-relativistic treatment of this problem and obtain exact solutions for various forms of the equation of state connecting the radial and tangential pressures. It is shown that pressure anisotropy can have significant effects on the structure and properties of stellar objects. In particular, the maximum value of 2M / R can approach unity (2M / R < 8/9 for isotropic objects) and the surface redshift can be arbitrarily large.