A GENERAL-RELATIVISTIC HYDROSTATIC MODEL FOR A GALAXY

A general relativistic, hydrostatic, and asymptotically flat model for a galaxy is studied. It considers four spherically symmetric regions, properly matched and with a specific profile density assigned to each one of them. We assume that the galaxy is dominated by the dark mass everywhere except at the nucleus, where the visible matter prevails. I n our model, the luminous matter located outside the nucleus of the ga laxy behaves as test particles orbiting in a dark matter bath and its orbital velocity grows slowly with distance. The end of the galaxy is marked by the vanishing of the pressure. In our model, this condition generates a jump in the density at the outer region of the galaxy and, as a consequence, a change in the slope of the orbital velocity of te st particles there. The specific shape of this bump depends on the mod el used. In our case, the inner structure of the galaxy is constructed following the observational data and the existence of this outer over density is proved on general grounds. This feature of the model seems to exist in a set of galaxies that displays a bump in the orbital velo city at the farthest end of their observed region. This effect, if it exists, may be difficult to single out from the background noise of th e data. The sudden jump in the density introduced by this model is pro posed here as a possible source for the gamma-ray bursts detected by t he Burst and Transient Source Experiment (BATSE). In this case, the ov erdensity would contain, eventually, a halo of neutron stars lying at the edge of our Galaxy. The model is scale-invariant and for this reas on can be applied to other cases of physical interest. We have also co mpared our results with those obtained with the Newtonian isothermal s phere.