Search Results (3)

This study numerically explores the dynamics of the photogravitational circular restricted three-body problem, where an infinitesimal particle moves under the gravitational influence of two primary bodies connected by a massless rod. These primary masses revolve in circular orbits around their common center of mass, which remains fixed at the origin of the coordinate system. The distance between the two masses remains constant, independent of their rotation period. The third body, being infinitesimally small compared to the primary masses, has a negligible effect on their motion. The primary mass is considered as a radiating body, while the secondary is modeled as an elongated one comprising two hypothetical point masses separated by a fixed distance. The analysis focuses on determining the number, location, and stability of equilibrium points, as well as examining the structure of zero-velocity curves under the influence of system parameters such as mass and force ratio, radiation pressure and geometric configuration of the secondary body. The system is found to allow up to six equilibria: four collinear and two non-collinear. Their number and positions are significantly affected by variations in the system’s parameters. Stability analysis reveals that the two non-collinear equilibrium points can exhibit stability under specific parameter configurations, while the four collinear points are typically unstable. An exception is the innermost collinear equilibrium point, which can be stable for certain parameter values. Our numerical investigation on periodic orbits around the collinear equilibrium points of the asteroid triple-system 2001SN₂₆₃ show that a variation, either to the values of radiation or the force ratio parameters, influence their special characteristics such as period and stability. Also, their continuation in the space of initial conditions shows that all families terminate naturally at collision orbits with either the primary or the secondary. Full article

The many problems faced by the theory of general relativity (GR) have always motivated us to explore the modified theory of GR. Considering the importance of studying the black hole (BH) entropy and its correction in gravity physics, we study the correction of thermodynamic entropy for a kind of spherically symmetric black hole under the generalized Brans–Dicke (GBD) theory of modified gravity. We derive and calculate the entropy and heat capacity. It is found that when the value of event horizon radius $r_{+}$ is small, the effect of the entropy-correction term on the entropy is very obvious, while for larger values $r_{+}$, the contribution of the correction term on entropy can be almost ignored. In addition, we can observe that as the radius of the event horizon increases, the heat capacity of BH in GBD theory will change from a negative value to a positive value, indicating that there is a phase transition in black holes. Given that studying the structure of geodesic lines is important for exploring the physical characteristics of a strong gravitational field, we also investigate the stability of particles’ circular orbits in static spherically symmetric BHs within the framework of GBD theory. Concretely, we analyze the dependence of the innermost stable circular orbit on model parameters. In addition, the geodesic deviation equation is also applied to investigate the stable circular orbit of particles in GBD theory. The conditions for the stability of the BH solution and the limited range of radial coordinates required to achieve stable circular orbit motion are given. Finally, we show the locations of stable circular orbits, and obtain the angular velocity, specific energy, and angular momentum of the particles which move in circular orbits. Full article

In the curved space-time, the neutral test particle is not affected by any other force except for the influence of the curved space-time. Similar to the free sub in the flat space, the Lagrangian of the test particle only contains the kinetic energy term—the kinetic energy term of the four-dimensional curved space-time. In the case of small space-time curvature, linear approximation can be made. That is, under the weak field approximation, the Lagrangian quantity degenerates into the Lagrangian quantity in the axisymmetric gravitational field in Newtonian mechanics. In this paper, the curved space-time composed of axisymmetric equidistant black holes is taken as a model. We study the geodesic motion of the test particles around three black holes with equal mass and static axisymmetric distribution, including time-like particles and photons. The three extreme Reissner–Nordstrom black holes are balanced by electrostatic and gravitational forces. We first give the geodesic motion equation of particles in Three black holes space-time, give the relativistic effective potential, discuss the possible motion state of particles, and classify their motion trajectories. Then, the particle motion of the special plane (equatorial plane) is studied. The circular orbits of the two types of particles in the symmetric plane are studied, respectively. The circular orbits outside the symmetric plane are also studied, and their stability is also discussed. We will show the influence of the separation distance of the three black holes on the geodesic motion and explore the change of the relativistic effective potential. Then, the relationship between the inherent quantity and the coordinate quantity in space-time is analyzed. Finally, the chaos of the test particle orbit is explored. Full article