On the active gravitational mass of a non-spherical source leaving hydrostatic equilibrium

We obtain an expression for the active gravitational mass (Tolman) of a source of the gamma metric, just after its departure from hydrostatic equilibrium, on a time scale of the order of (or smaller than) the hydrostatic time scale. It is shown that for very compact sources, even arbitrarily small departures from sphericity produce a significant decrease (increase) in the value of an active gravitational mass of collapsing (expanding) spheres, with respect to its value in equilibrium, enhancing thereby the stability of the system.