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Recent researches suggest an analogy between the theory of general relativity(GR) and fluid dynamics. As a result of this analogy, the Navier-Stokesequations and Einstein field equations are the same, and it is possible tostudy the properties of space-time by using fluid mechanics. In this paper, wepresent a new model to describe gravitational phenomena by an inviscid andcompressible fluid called space-time fluid (STF). The analogy method is used toobtain the gravity field of both static and rotating masses from the flow fieldof STF around static and rotating point sinks. In addition, event horizons andthe ergosphere of stationary black holes are defined based on our STF model.Then, we compare hydrodynamic forces exerted on a test particle withgravitational forces in the gravitoelectromagnetic approximation of the GR. Asa natural consequence, it is shown that inertial and gravitational masses areequivalent in this analogy. Finally, using the aspect of fluid dynamics, Mach'sprinciple, weak equivalence principle, and information discontinuity on theevent horizon are discussed.

An analogical model for the stationary black holes by the flow field of space-time fluid around a 3-dimensional point sink