Orbital stability of the restricted three body problem in General Relativity

We consider the problem of orbital stability of the motion of a test particle in the restricted three-body problem, by using the orbital moment and its time derivative. We show that it is possible to get some insight into the stability properties of the motion of test particles, without knowing the exact solutions of the motion equations.Comment: 2 page

The stability of orbit of a planet in the field of binary stars

In the paper, we consider the motion of a planet in the field of the binary stars in the theory of general relativity (GR), when all bodies have their own rotation. We consider that the third body moves in the plan of massive two bodies. The binary system orbit around the center of mass (sometimes referred to as the barycenter), in a circular orbit. The third body orbits closer to the primary star and does not affect the orbit of the secondary body. In fact, this problem belongs to the gravitational restricted three-body problem. We investigate the stability of the circular orbit of the planet in the binary system using the adiabatic theory of motion. The adiabatic theory of motion of bodies is the approach to study the evolutionary motion of bodies in the GR. The corresponding theory based on the vector elements of orbit to describe the motion of bodies and based on the asymptotic methods of nonlinear oscillations and in the method of adiabatic invariants

The orbital stability of a test body motion in the field of two massive bodies

We investigate the orbital stability of a test particle motion in the restricted three-body problem where all bodies have their own rotation. We have shown that it is possible to get some insight into the stability properties of the motion of test particles in restricted three-body problem, without knowing the exact solutions of the relativistic motion equations. © The Authors, published by EDP Sciences, 2018

The orbital stability of a test body motion in the field of two massive bodies

We investigate the orbital stability of a test particle motion in the restricted three-body problem where all bodies have their own rotation. We have shown that it is possible to get some insight into the stability properties of the motion of test particles in restricted three-body problem, without knowing the exact solutions of the relativistic motion equations. © The Authors, published by EDP Sciences, 2018

Dyon-Like Black Hole Solutions in the Model with Two Abelian Gauge Fields

Dilatonic black hole dyon-like solutions are overviewed in the gravitational 4D model with a scalar field, two 2-forms, two dilatonic coupling constants λi ≠ 0, i = 1, 2, obeying λ1 ≠ − λ2, and the sign parameter ε = ±1 before the scalar field kinetic term. Here ε = −1 corresponds to a phantom scalar field. The solutions are defined up to solutions of two master equations for two moduli functions, when λi2≠1/2 for ε = −1. Several integrable cases, corresponding to the Lie algebras A1 + A1, A2, B2 = C2 and G2 are considered. Some physical parameters of the solutions are derived: the gravitational mass, scalar charge, Hawking temperature, black hole area entropy and PPN parameters β and γ. Bounds on the gravitational mass and scalar charge, based on a certain conjecture, are presented. © 2019, Pleiades Publishing, Ltd

On the equivalence of approximate stationary axially symmetric solutions of the Einstein field equations

We study stationary axially symmetric solutions of the Einstein vacuum field equations that can be used to describe the gravitational field of astrophysical compact objects in the limiting case of slow rotation and slight deformation. We derive explicitly the exterior Sedrakyan–Chubaryan approximate solution, and express it in an analytical form, which makes it practical in the context of astrophysical applications. In the limiting case of vanishing angular momentum, the solution reduces to the well-known Schwarzschild solution in vacuum. We demonstrate that the new solution is equivalent to the exterior Hartle–Thorne solution. We establish mathematical equivalence between the Sedrakyan–Chubaryan, Fock–Abdildin and Hartle–Thorne formalisms. © 2016, Pleiades Publishing, Ltd

On the equivalence of approximate stationary axially symmetric solutions of the Einstein field equations

We study stationary axially symmetric solutions of the Einstein vacuum field equations that can be used to describe the gravitational field of astrophysical compact objects in the limiting case of slow rotation and slight deformation. We derive explicitly the exterior Sedrakyan–Chubaryan approximate solution, and express it in an analytical form, which makes it practical in the context of astrophysical applications. In the limiting case of vanishing angular momentum, the solution reduces to the well-known Schwarzschild solution in vacuum. We demonstrate that the new solution is equivalent to the exterior Hartle–Thorne solution. We establish mathematical equivalence between the Sedrakyan–Chubaryan, Fock–Abdildin and Hartle–Thorne formalisms. © 2016, Pleiades Publishing, Ltd

Effects of non-linear electrodynamics of vacuum in the magnetic quadrupole field of a pulsar

In this work, the non-linear effect of the magnetic dipole and quadrupole fields on the propagation of electromagnetic waves in the eikonal approximation of the parametrized post-Maxwell electrodynamics of the vacuum is calculated. Equations of motion for electromagnetic pulses transmitted in a strong magnetic field of a pulsar by two normal modes with mutually orthogonal polarization are constructed. The difference Δt in propagation times of normal waves from the common source of electromagnetic radiation to the receiver is calculated. It is shown that the forward part and the 'tail' by length cΔt of any hard radiation pulse due to the non-linear electromagnetic influence of the magnetic dipole and quadrupole fields turn out to be linearly polarized in mutually perpendicular planes, and the remaining part of the pulse must have elliptical polarization. © 2018 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society