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Recently, gravitational microlensing has been investigated in the framework of the weak field limit of fourth order gravity theory. However, solar system data (i.e. planetary periods and light bending) can be used to put strong constraints on the parameters of this class of gravity theories.We find that these parameters must be very close to those corresponding to the Newtonian limit of the theory.

Recently, Zakharov et al. (2005a, New Astron., 10, 479) considered the possibility of evaluating the spin parameter and the inclination angle for Kerr black holes in nearby galactic centers by using future advanced astrometrical instruments. A similar approach which uses the characteristic properties of gravitational retro-lensing images can be followed to measure the charge of a Reissner-Nordström black hole. Indeed, in spite of the fact that their formation might be problematic, charged black holes are objects of intensive investigations. From a theoretical point of view, it is well-known that a black hole is described by only three parameters, namely, its mass M, angular momentum J, and charge Q. Therefore, it would be important to have a method for measuring all these parameters, preferably by independent model of any. In this paper, we propose a procedure to measure the black hole charge by using the size of the retro-lensing images that can be revealed by future astrometrical missions. A discussion of the Kerr-Newmann black hole case is also offered.

The existence of dark matter (DM) at scales of few pc down to ≃ 10 −5 pc around the centers of galaxies and in particular in the Galactic Center region has been considered in the literature.Under the assumption that such a DM clump, principally constituted by non-baryonic matter (like WIMPs) does exist at the center of our galaxy, the study of the γ-ray emission from the Galactic Center region allows us to constrain both the mass and the size of this DM sphere.Further constraints on the DM distribution parameters may be derived by observations of bright infrared stars around the Galactic Center. Hall and Gondolo [1] used estimates of the enclosed mass obtained in various ways and tabulated by Ghez et al. [2,3]. Moreover, if a DM cusp does exist around the Galactic Center it could modify the trajectories of stars moving around it in a sensible way depending on the DM mass distribution. Here, we discuss the constraints that can be obtained with the orbit analysis of stars (as S2 and S16) moving inside the DM concentration with present and next generations of large telescopes. In particular, consideration of the S2 star apoastron shift may allow improving limits on the DM mass and size.