On the Movement of a Fluid with a Negative Pressure under the Action of its Own Gravitational Field
We have considered in the nonrelativistic approach the movement of the three types of the ﬂuid with negative pressure (cosmic vacuum, quintessence, Chaplygin gas) under the action of the own gravitational ﬁeld. Introduction in cosmological models of a substance with negative pressure is one of alternative approaches to the explanation of existence of the accelerated expansion of the Universe. The space vacuum possesses not only a certain density of energy, but also a pressure. If density of space vacuum is positive, its pressure is negative. Connection between pressure and density, i.e. the equation of state, has an appearance for vacuum P + = 0. This equation of state is compatible with the deﬁnition of vacuum as energy form with everywhere and always constant density, irrespective of frame of reference. Study of properties of such ﬂuids represents certain scientiﬁc interest from the point of view of existence of usual hydrodynamic properties, in particular, existence of wave movements under the action of the own gravitational ﬁeld. The movement of the ﬂuids with constant negative pressure is considered in spherical coordinates when only radial component of velocity u(r,t) is considered. We have established that for ﬂuid type space vacuum with constant negative pressure the movement is possible only if the source function doesn’t depend on coordinates. In this case the velocity of the ﬂuid is linear function of the distance from the beginning of coordinates that reminds Hubble’s law in cosmology. For ideal ﬂuid with the equation of state of the type of quintessential we have established that movement of the ﬂuid under the action of the own gravitational ﬁeld for one-dimensional movement is possible in the case if its density exceeds some critical value, the movement of the ﬂuid takes place in some bounded region 0 ≤ x ≤ xmax and its velocity changes from some critical value ucr to u = 0. We also studied the movement of the medium with the equation of state of the Chaplygin gas under its own gravitational ﬁeld in one-dimensional case, and show that there are three diﬀerent ﬂow regimes.