Analytic solutions for static spherically symmetric distribution of liquid in its gravitational self-field

Tolman's differential equations for the two components of the metric tensor of a spherically symmetric distribution of liquid are reduced to equations for two functions in which the derivative of one of them is expressed in terms of the other, and not only the components of the metric tensor but also the physical characteristics of the continuous medium are expressed in terms of these functions. Arbitrary choice of the second function generates different self-consistent solutions. By means of the simplest choices of this function, two single-parameter solutions are found – one for a gas and the other for a liquid.