相关论文: Circular Orbits under Central Forces in Special Re…
The stability of the dynamical trajectories of softened spherical gravitational systems is examined, both in the case of the full $N$-body problem and that of trajectories moving in the gravitational field of non-interacting background…
We study point particles in 2+1 dimensional first order gravity using a triangulation to fix the connection and frame-field. The Hamiltonian is reduced to a boundary term which yields the total mass. The triangulation is dynamical with…
A self-propelled particle in a two-dimensional axisymmetric system, such as a particle in a central force field or confined in a circular region, may show rotational or oscillatory motion. These motions do not require asymmetry of the…
We study the geometric effects of our galaxy's peculiar motion on the circles-in-the-sky. We show that the shape of these circles-in-the-sky remains circular, as detected by a local observer with arbitrary peculiar velocity. Explicit…
In the curved spacetime background, the trajectory of a spinning test particle will deviate from the geodesic. Using the effective potential method, we study the motion of a spinning test particle on the equatorial plane of a polymer black…
Recent developments on the rotational instabilities of relativistic stars are reviewed. The article provides an account of the theory of stellar instabilities with emphasis on the rotational ones. Special attention is being paid to the…
Equatorial circular geodesic orbits of neutral test particles in the exterior spacetime of a charged rotating disc of dust are analyzed in dependence of its specific charge and a relativity parameter. The charged rotating disc of dust is an…
Bertrand's theorem proves that inverse square and Hooke's law-type central forces are the only ones for which all bounded orbits are closed. Similar analysis was used to show that for other central force laws there exist closed orbits for a…
We investigate the influence of a gravitational wave background on particles in circular motion. We are especially interested in waves leading to stationary orbits. This consideration is limited to circular orbits perpendicular to the…
Newton's theorem of revolving orbits states that one can multiply the angular speed of a Keplerian orbit by a factor $k$ by applying a radial inverse cubed force proportional to $(1-k^2)$. In this paper we derive an extension of this…
We study the dynamics of $N$ point vortices on a rotating sphere. The Hamiltonian system becomes infinite dimensional due to the non-uniform background vorticity coming from the Coriolis force. We prove that a relative equilibrium formed of…
Motion of test particles along rotating curved trajectories is considered. The problem is studied both in the laboratory and the rotating frames of reference. It is assumed that the system rotates with the constant angular velocity $\omega…
In the present paper we investigate self-consistently slowly rotating neutron and strange stars in R-squared gravity. For this purpose we first derive the equations describing the structure of the slowly rotating compact stars in…
We study non-geodesic orbits of test particles endowed with a structure, assuming the Schwarzschild spacetime as background. We develop a formalism which allows one to recognize the geometrical characterization of those orbits in terms of…
Existence of a photon circular orbit can tell us a lot about the nature of the underlying spacetime, since it plays a pivotal role in the understanding of the characteristic signatures of compact objects, namely the quasi-normal modes and…
We investigate general relativistic effects associated with the gravitomagnetic monopole moment of gravitational source through the analysis of the motion of test particles and electromagnetic fields distribution in the spacetime around…
In the spacetime of horizonless compact objects described by Einsteinian cubic gravity (ECG), we demonstrate the existence of static stable timelike circular orbits on which massive particles remain at rest relative to distant observers.…
In this new era of gravitational wave astrophysics, observations have indicated the likely existence of black holes with significant spin. In order to better understand the potential imprint orbital dynamics have on the multi-messenger…
In this paper we investigate the innermost stable circular orbit (ISCO) for a classical spinning test particle in the background of Kerr-Newman black hole. It is shown that the orbit of the spinning particle is related to the spin of the…
Newton famously showed that a gravitational force inversely proportional to the square of the distance, $F \sim 1/r^2$, formally explains Kepler's three laws of planetary motion. But what happens to the familiar elliptical orbits if the…