Narrow Results

We consider the quasi-classical model of the spin-free configuration on the basis of the self-gravitating spherical dust shell in general relativity. For determination of the energy spectrum of the stationary states on the basis of quasi-classical quantization rules it is required to carry out some regularization of the system. It is realized by an embedding of the initial system in the extended system with rotation. Then, the stationary states of the spherical shells are S-states of the system with the intrinsic momentum. The quasi-classical treatment of a stability of the configuration is associated with the Langer modification of a square of the quantum mechanical intrinsic momentum. It gives value of critical bare mass of the shell determining threshold of stability. For the shell with the bare mass smaller or equal to the Planck's mass, the energy spectra of bound states are found. We obtain the expression for tunneling probability of the shell and construct the quasi-classical model of the pair creation and annihilation of the shells.

Applying the Damour–Soffel–Xu framework of general-relativistic celestial mechanics, the theory of relativistic rigid body presented by Thorne and Gürsel is extended and developed in this paper. We successfully construct a quasi-rigid body model in the full post-Newtonian framework for the first time. This model has some simple properties in a similar way to the Newtonian rigid body, and it could be applied in geodynamics and astronomy, for example, to solve problems on rotation or precession of celestial bodies when relativistic effects are not negligible.

General relativistic equilibrium conditions imply that an electrically charged compact star, in a spherically symmetric configuration, can sustain a huge amount of electric charge (up to 10²⁰ C). The equilibrium, however, is reached under very critical conditions such that a perturbation to the stellar structure can cause these systems to collapse. We study the effects of rotation in charged compact stars and obtain conditions, the modified Tolman–Oppenheimer–Volkoff (TOV) equations, under which such stars form a stable gravitational system against Coulomb repulsion. We assume the star to be rotating slowly. We also assume that the charge density is proportional to the mass density everywhere inside the star. The modified TOV equations for hydrostatic equilibrium are integrated numerically for the general equation of state for a polytrope. The detailed numerical study shows that the centrifugal force adds to the Coulomb pressure in the star. In the stable equilibrium configurations, therefore, a loss in stellar mass (energy) density occurs for higher values of the angular frequency. The additional energy is radiated in the form of electrical energy. The stellar radius is also decreased so that the star does not necessarily becomes more compact.

Internally rotating jets are expected to be present in a number of astrophysical sources including AGNs. Here we consider the acceleration of energetic charged particles within such flows and discuss the role of shear and centrifugal effects for efficient particle energization. We show that in the case of significant rotation, centrifugal effects could play an important role and facilitate efficient acceleration near the spine of the jet. We point out that shear acceleration could be particularly interesting in the context of hadronic models.

Rotation and Dirac spin coupling is described by the tetrad field for a rotating system, where the rotation-spin effect is replaced by an axial torsion-spin. After constructing a rotating tetrad field, we derive the torsion quantities, by which we deal with the torsion-spin coupling.

Employing higher-order perturbation theory, we find a new class of perturbative extremal rotating black hole solutions with Born–Infeld electric charge in odd D dimensional spacetime. The seed solution is an odd-dimensional extremal Myers–Perry black hole with equal angular momenta to which a perturbative, nonlinear, electric Born–Infeld field charge q is added maintaining the extremality condition. The perturbations are performed up to third-order. We also study some physical properties of these black holes. In particular, it is shown that the values of the gyromagnetic ratio of the black holes are modified by the perturbative parameter q and the Born–Infeld parameter β.

We calculate moment of inertia of neutron star with different exotic constituents such as hyperons and antikaon condensates and study its variation with mass and spin frequency. The sets of equation-of-state (EoS), generated within the framework of relativistic mean field model with density-dependent couplings are adopted for the purpose. We follow the quasi-stationary evolution of rotating stars along the constant rest mass sequences, that varies considerably with different constituents in the EoS. We also explore the universal relations associated with some of the normalized properties, such as critical mass and moment of inertia for specific EoS or as a matter of fact constituents of the dense matter. Deviations in the universal relations for moment of inertia are observed at higher compactness. This study presents important results concerning the properties of neutron stars, that could be observationally verified in the near future using Square Kilometer Array telescope.

The well-known problem of wormholes in General Relativity (GR) is the necessity of exotic matter, violating the Weak Energy Condition (WEC), for their support. This problem looks easier if, instead of island-like configurations, one considers string-like ones, among them, cylindrically symmetric spacetimes with rotation. However, for cylindrical wormhole solutions, a problem is the lacking asymptotic flatness, making it impossible to observe their entrances as local objects in our universe. It was suggested to solve this problem by joining a wormhole solution to flat asymptotic regions at some surfaces ${\mathrm{\Sigma }}_{-}$ and ${\mathrm{\Sigma }}_{+}$ on different sides of the throat. The configuration then consists of three regions, the internal one containing a throat and two flat external ones. We discuss different kinds of source matter suitable for describing the internal regions of such models (scalar fields, isotropic and anisotropic fluids) and present two examples where the internal matter itself and the surface matter on both junction surfaces ${\mathrm{\Sigma }}_{\pm }$ respect the WEC. In one of these models, the internal source is a stiff perfect fluid whose pressure is equal to its energy density, in the other, it is a special kind of anisotropic fluid. Both models are free from closed timelike curves. We thus obtain examples of regular twice asymptotically flat wormhole models in GR without exotic matter and without causality violations.

In this study, we have considered Gödel universe in the context of $f(R,T)$ modified theory of gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$ and the trace of the energy–momentum tensor $T$. We have shown that the Gödel solution exists in this modified theory for more general functional form of $f(R,T)$ function than it appears in the literature.

In this paper, the effect of dissipative energy arising from bulk-viscosity on the collapse of a self-gravitating viscoelastic medium permeated with a nonuniform magnetic field and rotation is analyzed using the standard Jeans mechanism. A local solution of the system of nondimensional linearized perturbation equations, having variable coefficients, is obtained using the normal modes analysis method. The Jeans instability criteria are derived from the characteristic equation (valid under the kinetic and hydrodynamic limits) for parallel and perpendicular wave propagation, modified due to bulk viscosity and Alfvén wave velocity. From the calculated critical values of Jeans wavenumber, it is found that the bulk-viscosity and magnetic field have stabilizing influence on the onset of gravitational instability for each mode of wave propagation. It is observed that the nonuniform rotation does not affect the instability criterion, however, the rotation strongly suppresses the growth rate of the Jeans instability in both the hydrodynamic and kinetic limits. Also, a comparison of the impact of various rotational and magnetic field orientations on the growth rate in viscoelastic fluid is also presented. From the analysis, it is also observed that the presence of dissipative energy reduces the growth rate, in both modes of wave propagation.