Uros Kostic

On the tidal evolution of the orbits of low-mass satellites around black holes

Context. Low-mass satellites, like asteroids and comets, are expected to be present around the black hole at the Galactic center. We consider small bodies orbiting a black hole, and we study the evolution of their orbits due to tidal interaction with the black hole. Aims. In this paper we investigate the consequences of the existence of plunging orbits when a black hole is present. We are interested in finding the conditions that exist when capture occurs. Methods. Earlier analysis of the evolution of classical Keplerian orbits was extended to relativistic orbits around a Schwarzschild black hole. Results. The main difference between the Keplerian and black hole cases is in the existence of plunging orbits. Orbital evolution, leading from bound to plunging orbits, goes through a “final” unstable circular orbit. On this orbit, tidal energy is released on a characteristic black hole timescale. Conclusions. This process may be relevant for explaining how small, compact clumps of material can be brought onto plunging orbits, where they may produce individual short duration accretion events. The available energy and the characteristic timescale are consistent with energy released and the timescale typical of Galactic flares.

Optics in the Schwarzschild spacetime

Realistic modeling of radiation transfer in and from variable accretion disks around black holes requires the solution of the problem: find the constants of motion and equation of motion of a lightlike geodesic connecting two arbitrary points in space. Here we give the complete solution of this problem in the Schwarzschild spacetime.

Relativistic Positioning System in perturbed spacetime

We present a variant of a Global Navigation Satellite System called a Relativistic Positioning System (RPS), which is based on emission coordinates. We modelled the RPS dynamics in a space-time around Earth, described by a perturbed Schwarzschild metric, where we included the perturbations due to Earth multipoles (up to the 6th), the Moon, the Sun, Venus, Jupiter, solid tide, ocean tide, and Kerr rotation effect. The exchange of signals between the satellites and a user was calculated using a ray-tracing method in the Schwarzschild space-time. We find that positioning in a perturbed space-time is feasible and is highly accurate already with standard numerical procedures: the positioning algorithms used to transform between the emission and the Schwarzschild coordinates of the user are very accurate and time efficient -- on a laptop it takes 0.04 s to determine the users spatial and time coordinates with a relative accuracy of

Do flares in Sagittarius A* reflect the last stage of tidal capture?

10^{-28}-10^{-26}

Tidal effects in the vicinity of a black hole

and

Modelling the light-curves of objects tidally disrupted by a black hole

10^{-32}-10^{-30}

Tidal Capture by a Black Hole and Flares in Galactic Centres

, respectively.

Clumps of material orbiting a black hole and the QPOs

In recent years the case for the presence of 3 – 4 × 106M⊙ black hole in our Galactic Center has gain strength from results of stellar dynamics observations and from the detection of several rapid X‐ray and IR flares observed in the Sagittarius A* from 2000 to 2004. Here we explore the idea that such flares are produced when the central black hole tidally captures and disrupts a small body — e.g. a comet or an asteroid.

Numerical modeling of a Global Navigation Satellite System in a general relativistic framework

The discovery that the Galactic centre emits flares at various wavelengths represents a puzzle concerning their origin, but at the same time it is a relevant opportunity to investigate the environment of the nearest super‐massive black hole. In this paper we shall review some of our recent results concerning the tidal evolution of the orbits of low mass satellites around black holes, and the tidal effect during their in‐fall. We show that tidal interaction can offer an explanation for transient phenomena like near infra‐red and X‐ray flares from Sgr A*.

Analytical time-like geodesics in Schwarzschild space-time

Tidal disruption by massive black holes is a phenomenon, during which a large part of gravitational energy can be released on a very short time-scale. The time-scales and energies involved during X-ray and IR flares observed in Galactic centre suggest that they may be related to tidal disruption events. Furthermore, aftermath of a tidal disruption of a star by super-massive black hole has been observed in some galaxies, e.g. RX J1242.6-1119A. All these discoveries increased the demand for tools for tidal disruption study in curved space-time. Here we summarise our study of general relativistic effects on tidal deformation of stars and compact objects.