Under the assumptions that molecular clouds are nearly spatially and temporally isothermal and that the density peaks (``cores) within them are formed by turbulent fluctuations, we argue that cores cannot reach a hydrostatic (or magneto-static) state as a consequence of their formation process. In the non-magnetic case, stabilization requires a Bonnor-Ebert truncation at a finite radius, which is not feasible for a single-temperature flow, unless it amounts to a shock, which is clearly a dynamical feature. Instead, in this case, cores must be dynamical entities that can either be pushed into collapse, or else ``rebound towards the mean pressure and density as the parent cloud. Nevertheless, rebounding cores are delayed in their re-expansion by their own self-gravity. We give a crude estimate for the re-expansion time as a function of the closeness of the final compression state to the threshold of instability, finding typical values $sim 1$ Myr, i.e., of the order of a few free-fall times. Our results support the notion that not all cores observed in molecular clouds need to be on route to forming stars, but that instead a class of ``failed cores should exist, which must eventually re-expand and disperse, and which can be identified with observed starless cores. In the magnetic case, recent observational and theoretical work suggests that all cores are critical or supercritical, and are thus qualitatively equivalent to the non-magnetic case. Our results support the notion that the entire star formation process is dynamical, with no intermediate hydrostatic stages.
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