Narrow Results

We investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic expressions for the orbital angular velocity, the specific angular momentum and energy, and the radii of marginally stable and marginally bound circular orbits. Moreover, we calculate the orbital angular velocity and the radius of lightlike circular geodesics. We study numerically the frame dragging effect and the influence of the quadrupolar deformation of the source on the motion of test particles. We show that the effects originating from the rotation can be balanced by the effects due to the oblateness of the source.

In this work, we report the results from our spectroscopic study on AlF and AlCl molecules. We carry out detailed electronic structure calculations in both the molecules, including obtaining the potential energy surfaces of the $X^1\mathrm{\Sigma }$ ground electronic state and some of the low-lying excited electronic states belonging to $\mathrm{\Sigma }$ and $\mathrm{\Pi }$ symmetries. This is followed by evaluating the spectroscopic constants and molecular properties such as electric dipole moments and electric quadrupole moments. Throughout, we employ the multi-reference configuration interaction method and work with high-quality quadruple zeta basis sets. Further, transition dipole moments between the ground electronic state and singlet excited states are also studied. The relevant vibrational parameters are computed by solving the vibrational Schrödinger equation. Subsequently, the vibrational energy spacings and transition dipole moments between the vibrational levels belonging to the same electronic states are used to evaluate the spontaneous and black-body radiation-induced transition rates, followed by computing the lifetimes. Finally, the energy differences between rotational levels belonging to different vibrational levels and within an electronic state as well as the Einstein coefficients are reported.

We present the Gross–Pitaevskii equation for Bose–Einstein condensates (BECs) possessing the electric dipole and the electric quadrupole moments in a non-integral form. These equations are coupled with the Maxwell equations. The model under consideration includes the dipole–dipole, the dipole–quadrupole, and the quadrupole–quadrupole interactions in terms of the electric field created by the dipoles and quadrupoles. We apply this model to obtain the Bogoliubov spectrum for three-dimensional BECs with a repulsive short-range interaction. We obtain an extra term in the Bogoliubov spectrum in comparison with the dipolar BECs. We show that the quadrupole–quadrupole interaction gives a positive contribution in the Bogoliubov spectrum. Hence, this spectrum is stable.

We investigate the gravitational field of a static mass with quadrupole moment in empty space. It is shown that in general this configuration is characterized by the presence of curvature singularities without a surrounding event horizon. These naked singularities generate an effective field of repulsive gravity which, in turn, drastically changes the behavior of test particles. As a possible consequence, the accretion disk around a naked singularity presents a particular discontinuous structure.

Equilibrium sequences were developed for rotating neutron stars in the relativistic mean-field interaction framework using four density-dependent equations of state (EOSs) for the neutron star matter. These sequences were constructed for the observed rotation frequencies of 25, 317, 346, 716 and 1122Hz. The bounds of sequences, the secular axisymmetric instability, static and Keplerian sequences were calculated in each model to determine the stability region. The gravitational mass, quadrupole moment, polar, forward and backward redshifts, and Kerr parameter were calculated according to this stability region, and the allowable range of these quantities was then determined for each model. According to the results, DDF and DD-ME$\delta$ were unable to properly describe the low-frequency neutron stars, PSR J0348+432, PSR J1614-2230 and PSR J0740+6620 rotate at a frequency of 25, 317 and 346Hz, respectively. On the other hand, all the selected EOSs properly described the rotation of PSR J1748-244ad and PSR J1739-285 at a frequency of 716 and 1122Hz, respectively. The mass of these stars was, therefore, in the range of $[0.68,2.14]M_{\odot }$ and $[1.67,2.24]M_{\odot }$, respectively. The polar, forward and backward redshifts, and the quadrupole moment were calculated in all the selected rotating frequencies and the Keplerian sequence. The results were consistent with observations. Confirming the mass of $1.5_{-1.0}^{+0.4}{M}_{\odot }$ for EXO 0748-676, our result, $Z_P\approx 0.3$, will be close to the observed value, and the EOSs used in this study properly describe this star. Interestingly, the extremum of Kerr parameter, polar, forward and backward redshifts in all models reached constant values of, $a/M\approx 0.7$, $Z_p\approx 0.8$, $Z_{\mathrm{\text{eq}}}^f\approx -0.3$ and $Z_{\mathrm{\text{eq}}}^b\approx 2.2$, respectively. These behaviors of redshifts and Kerr parameter are approximately independent of EOS. The observed behaviors must evaluate by other EOSs to find universal relations for these quantities. Also, a limit value was found for each of these parameters. In this case where these parameters are greater than the limit value, the star can rotate at a frequency equal to or greater than $\nu =1122$Hz.

We investigate the interior Einstein’s equations in the case of a static, axially symmetric, perfect fluid source. We present a particular line element that is specially suitable for the investigation of this type of interior gravitational fields. Assuming that the deviation from spherically symmetry is small, we linearize the corresponding line element and field equations and find several classes of vacuum and perfect fluid solutions. We find some particular approximate solutions by imposing appropriate matching conditions.

The properties of uniformly rotating white dwarfs are analyzed within the framework of general relativity. Hartle's formalism is applied to construct self-consistently the internal and external solutions to the Einstein equations. The mass, the radius, the moment of inertia and quadrupole moment of rotating white dwarfs have been calculated as a function of both the central density and rotation period of the star. The maximum mass of rotating white dwarfs for stable configurations has been obtained.

The deformation structure of the even–even ytterbium, hafnium and tungsten nuclei is investigated in framework of the collective model, the single-particle Schrödinger fluid model and the cranked Nilsson model. Accordingly, we have calculated the rotational and vibrational energies, the nuclear moments of inertia, the total ground-state energy, the quadrupole moment, the liquid drop (LD) energy, the Strutinsky inertia, the LD inertia, the volume conservation factor , the smoothed energy, the Bardeen, Cooper and Schrieffer (BCS) energy and the G-value of the ytterbium: ¹⁷⁰Yb, ¹⁷²Yb and ¹⁷⁴Yb, hafnium: ¹⁷⁶Hf, ¹⁷⁸Hf and ¹⁸⁰Hf and tungsten: ¹⁸²W, ¹⁸⁴W and ¹⁸⁶W nuclei as functions of the deformation parameters β, γ, which are assumed to vary in the ranges (-0.50 ≤ β ≤ 0.50) and (0° ≤ γ ≤ 60°). Also, two polynomials in β are obtained to produce results in good agreement with the corresponding results for the total ground-state energy and the quadrupole moment of the mentioned nine nuclei.

We present a static axisymmetric solution of Einstein’s field equations. Assuming that the deviation from spherically symmetry is small, we linearize the corresponding field equations with the perfect fluid source and up to the first order in quadrupole.

We consider a static and axially symmetric metric containing two quadrupole parameters. In the present contribution, we study the quadrupole moments constraints on the properties of the relativistic accretion disc models, also explore the relation of oscillatory frequencies of charged particles to the frequencies of the twin high-frequency quasi-periodic oscillations observed in some microquasars. We also compare the results with Schwarzschild and Kerr metrics.

We derive the rate of change of the mean motion up to the second post-Newtonian order for inspiralling compact binaries with spin, mass quadrupole and magnetic dipole moments on eccentric orbits. We give this result in terms of orbital elements. We also present the related orbital phase for circular orbits.

The radial component of the motion of compact binary systems composed of neutron stars and/or black holes on eccentric orbit is integrated. We consider all type of perturbations that emerge up to second post-Newtonian order. These perturbations are either of relativistic origin or are related to the spin, mass quadrupole and magnetic dipole moments of the binary components. We derive a generalized Kepler equation and investigate its domain of validity, in which it properly describes the radial motion.