Relativistic polytropic models of charged anisotropic compact objects

In this paper, we introduce new viable solutions to the Einstein-Maxwell field equations by incorporating the features of anisotropic matter distributions within the realm of the general theory of relativity (\begin{document}${\rm GR}$\end{document}). To obtain these solutions, we employed the Finch-Skea spacetime, along with a generalized polytropic equation of state (\begin{document}${\rm EoS}$\end{document}). We constructed various models of generalized polytropes by assuming different values of the polytropic index, i.e., \begin{document}$\eta= \dfrac{1}{2},~ \dfrac{2}{3},~ 1$\end{document}, and \begin{document}$ 2 $\end{document}. Next, numerous physical characteristics of these considered models were studied via graphical analysis, and they were found to obey all the essential conditions for astrophysical compact objects. Furthermore, such outcomes of charged anisotropic compact star models could be reproduced in various other cases including linear, quadratic, and polytropic \begin{document}${\rm EoS}$\end{document}     

Exploring physical features of anisotropic quark stars in Brans-Dicke theory with a massive scalar field via embedding approach

The main aim of this study is to explore the existence and salient features of spherically symmetric relativistic quark stars in the background of massive Brans-Dicke gravity. The exact solutions to the modified Einstein field equations are derived for specific forms of coupling and scalar field functions using the equation of state relating to the strange quark matter that stimulates the phenomenological MIT-Bag model as a free Fermi gas of quarks. We use a well-behaved function along with the Karmarkar condition for class-one embedding as well as junction conditions to determine the unknown metric tensors. The radii of strange compact stars viz., PSR J1416-2230, PSR J1903+327, 4U 1820-30, CenX-3, and EXO1785-248, are predicted via their observed mass for different values of the massive Brans-Dicke parameters. We explore the influences of the mass of scalar field \begin{document}$m_{\phi}$\end{document}, coupling parameter \begin{document}$\omega_{\rm BD}$\end{document}, and bag constant \begin{document}${\cal{B}}$\end{document} on state determinants and perform several tests on the viability and stability of the constructed stellar model. Conclusively, we find that our stellar system is physically viable and stable as it satisfies all the energy conditions and necessary stability criteria under the influence of a gravitational scalar field.     

Dark matter with chiral symmetry admixed with hadronic matterin compact stars

Using the two-fluid Tolman-Oppenheimer-Volkoff equation, the properties of dark matter (DM) admixed neutron stars (DANSs) have been investigated. In contrast to previous studies, we find that an increase in the maximum mass and a decrease in the radius of 1.4 \begin{document}$ M_\odot $\end{document} NSs can occur simultaneously in DANSs. This stems from the ability of the equation of state (EOS) for DM to be very soft at low density but very stiff at high density. It is well known that the IU-FSU and XS models are unable to produce a neutron star (NS) with a maximum mass greater than 2.0 \begin{document}$ M_\odot $\end{document}. However, by considering the IU-FSU and XS models for DANSs, there are interactions with DM that can produce a maximum mass greater than 2.0 \begin{document}$ M_\odot $\end{document} and a radius of 1.4 \begin{document}$ M_\odot $\end{document} NSs below 13.7 km. When considering a DANS, the difference between DM with chiral symmetry (DMC) and DM with meson exchange (DMM) becomes obvious when the central energy density of DM is greater than that of nuclear matter (NM). In this case, the DMC model with a DM mass of 1000 MeV can still produce a maximum mass greater than 2.0 \begin{document}$ M_\odot $\end{document} and a radius of a 1.4 \begin{document}$ M_\odot $\end{document} NS below 13.7 km. Additionally, although the maximum mass of the DANS using the DMM model is greater than 2.0 \begin{document}$ M_\odot $\end{document}, the radius of a 1.4 \begin{document}$ M_\odot $\end{document} NS can surpass 13.7 km. In the two-fluid system, the maximum mass of a DANS can be larger than 3.0 \begin{document}$ M_\odot $\end{document}. Consequently, the dimensionless tidal deformability \begin{document}$ \Lambda_{CP} $\end{document} of a DANS with 1.4 \begin{document}$ M_\odot $\end{document}, which increases with increasing maximum mass, may be larger than 800 when the radius of the 1.4 \begin{document}$ M_\odot $\end{document} DANS is approximately 13.0 km.     

Sound velocity in dense stellar matter with strangeness and compact stars

The phase state of dense matter in the intermediate density range (\begin{document}$\sim$\end{document}1-10 times the nuclear saturation density) is both intriguing and unclear and can have important observable effects in the present gravitational wave era of neutron stars. As matter density increases in compact stars, the sound velocity is expected to approach the conformal limit (\begin{document}$c_s/c=1/\sqrt{3}$\end{document}) at high densities and should also fulfill the causality limit (\begin{document}$c_s/c<1$\end{document}). However, its detailed behavior remains a prominent topic of debate. It was suggested that the sound velocity of dense matter could be an important indicator of a deconfinement phase transition, where a particular shape might be expected for its density dependence. In this work, we explore the general properties of the sound velocity and the adiabatic index of dense matter in hybrid stars as well as in neutron stars and quark stars. Various conditions are employed for the hadron-quark phase transition with varying interface tension. We find that the expected behavior of the sound velocity can also be achieved by the nonperturbative properties of the quark phase, in addition to a deconfinement phase transition. Moreover, it leads to a more compact star with a similar mass. We then propose a new class of quark star equation of states, which can be tested by future high-precision radius measurements of pulsar-like objects.     

Plane Symmetric Inhomogeneous Cosmological Models with a Perfect Fluid in General Relativity

In this paper we investigate a class of solutions of Einstein equations for the plane- symmetric perfect fluid case with shear and vanishing acceleration. If these solutions have shear, they must necessarily be non-static. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three classes of solutions. PACS No.: 04.20.-q.     

Exact Solutions to Three-Dimensional Schrödinger Equation with an Exponentially Position-Dependent Mass

For an exponentially position-dependent mass, we obtain the exact solutions of the three-dimensional Schrödinger equation by using coordinate transformation method for the reference problems with Coulomb potential, Kratzer potential, and spherically square potential well of infinite depth, respectively. The explicit expressions for the energy eigenvalues and the corresponding eigenfunctions of the three systems are presented.     

Form-Preserving Transformations of Time-Dependent Schrödinger Equation with Time- and Position-Dependent Mass

We study space-time transformations of the time-dependent Schrödinger equation (TDSE) with time- and position-dependent (effective) mass. We obtain the most general space-time transformation that maps such a TDSE onto another one of its kind. The transformed potential is given in explicit form.     

Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

We study the time-dependent Schrödinger equation (TDSE) with an effective (position-dependent) mass, relevant in the context of transport phenomena in semiconductors. The most general form-preserving transformation between two TDSEs with different effective masses is derived. A condition guaranteeing the reality of the potential in the transformed TDSE is obtained. To ensure maximal generality, the mass in the TDSE is allowed to depend on time also.