Hyperbolically symmetric static fluids: A general study

We carry on a comprehensive study static fluid distributions endowed with hyperbolical symmetry. Their physical properties are analyzed in detail. The energy density appears to be necessarily negative, which suggests that any possible application of this kind fluids requires extreme conditions where quantum effects expected play an important role. Also, it is found the distribution cannot fill region close center Such may represented by vacuum cavity around center. A suitable definition mass function, as well Tolman explicitly calculated. While former positive defined, latter negative most cases, revealing repulsive nature gravitational interaction. general approach obtain exact solutions presented and some analytical exhibited.