Brownian motion of black holes in stellar systems with non-Maxwellian distribution for the stars field

A massive black hole at the center of a dense stellar system, such as a globular cluster or a galactic nucleus, is subject to a random walk due gravitational encounters with nearby stars. It behaves as a Brownian particle, since it is much more massive than the surrounding stars and moves much more slowly than they do. If the distribution function for the stellar velocities is Maxwellian, there is a exact equipartition of kinetic energy between the black hole and the stars in the stationary state. However, if the distribution function deviates from a Maxwellian form, the strict equipartition cannot be achieved. The deviation from equipartition is quantified in this work by applying the Tsallis q-distribution for the stellar velocities in a q-isothermal stellar system and in a generalized King model.Comment: Presented at XXVI Int. Astronomical Union General Assembly, Symp. 238, Prague, Czech Republic, Aug 21-25 200

Gravity with extra dimensions and dark matter interpretation: A straightforward approach

Any connection between dark matter and extra dimensions can be cognizably evinced from the associated effective energy-momentum tensor. In order to investigate and test such relationship, a higher dimensional spacetime endowed with a factorizable general metric is regarded to derive a general expression for the stress tensor -- from the Einstein-Hilbert action -- and to elicit the effective gravitational potential. A particular construction for the case of six dimensions is provided, and it is forthwith revealed that the missing mass phenomenon may be explained, irrespective of the dark matter existence. Moreover, the existence of extra dimensions in the universe accrues the possibility of a straightforward mechanism for such explanation. A configuration which density profile coincides with the Newtonian potential for spiral galaxies is constructed, from a 4-dimensional isotropic metric plus extra-dimensional components. A Miyamoto-Nagai \emph{ansatz} is used to solve Einstein equations. The stable rotation curves associated to such system are computed, in full compliance to the observational data, without fitting techniques. The density profiles are reconstructed and compared to that ones obtained from the Newtonian potential.Comment: 13 pages, 6 figure