The radiation observed in quasars and active galactic nuclei is mainly produced by a relativistic plasma orbiting close to the black hole event horizon, where strong gravitational effects are relevant. The observational data of such systems can be compared with theoretical models to infer the black hole and plasma properties. In the comparison process, ray-tracing algorithms are essential to computing the trajectories followed by the photons from the source to our telescopes. In this paper, we present : a new stable FORTRAN code capable of efficiently computing null-geodesics around compact objects, including general relativistic effects such as gravitational lensing, redshift, and relativistic boosting. The algorithm is based on the Hamiltonian formulation and uses different integration schemes to evolve null-geodesics while tracking the error in the Hamiltonian constrain to ensure physical results. We found from an error analysis that the integration schemes are all stable, and the best one maintains an error below $$10^{-11}$$ 10 - 11 . Particularly, to test the robustness and ability of the code to evolve geodesics in curved space-time, we compute the shadow and Einstein rings of a Kerr black hole with different rotation parameters and obtain the image of a thin Keplerian accretion disk around a Schwarzschild black hole. Although is parallelized neither with MPI nor with CUDA, the computation times are of the same order as those reported by other codes with these types of parallel computing platforms.

The dynamics of the four-body problem have attracted increasing attention in recent years. In this paper, we extend the basic equilateral four-body problem by introducing the effect of radiation pressure, Poynting-Robertson drag, and solar wind drag. In our setup, three primaries lay at the vertices of an equilateral triangle and move in circular orbits around their common center of mass. Here, one of the primaries is a radiating body and the fourth body (whose mass is negligible) does not affect the motion of the primaries. We show that the existence and the number of equilibrium points of the problem depend on the mass parameters and radiation factor. Consequently, the allowed regions of motion, the regions of the basins of convergence for the equilibrium points, and the basin entropy will also depend on these parameters. The present dynamical model is analyzed for three combinations of mass for the primaries: equal masses, two equal masses, different masses. As the main results, we find that in all cases the libration points are unstable if the radiation factor is larger than 0.01 and hence able to destroy the stability of the libration points in the restricted four-body problem composed by Sun, Jupiter, Trojan asteroid and a test (dust) particle. Also, we conclude that the number of fixed points decreases with the increase of the radiation factor.

We study the effect of the radiation parameter in the location, stability and orbital dynamics in the Lagrange configuration of the restricted four-body problem when one of the primaries is a radiating body. The equations of motion for the test particle are derived by assuming that the primaries revolve in the same plane with uniform angular velocity, and regardless of their mass distribution, they will always lie at the vertices of an equilateral triangle. The insertion of the radiation factor in the restricted four-body problem, let us model more realistically the dynamics of a test particle orbiting an astrophysical system with an active star. The dynamical mechanisms responsible for the smoothening on the basin structures of the configuration space is related to the decrease in the total number of fixed points with increasing values of the radiation parameter. In our model of the Sun-Jupiter-Trojan Asteroid system, it is found that despite the repulsive character of the solar radiation pressure, there exist two stable libration points roughly located at the position ofL 4 and L 5 in the Sun-Jupiter system.