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We present the exact solutions for the collapse of a spherically-symmetric,cold (i.e., pressureless) cloud under its own self-gravity, valid for arbitraryinitial density profiles and not restricted to the realm of self-similarity.These solutions exhibit a number of remarkable features, including theself-consistent formation of and subsequent accretion onto a central pointmass. A number of specific examples are provided, and we show that Penston'ssolution of pressureless, self-similar collapse is recovered for polytropicdensity profiles; importantly, however, we demonstrate that the time over whichthis solution holds is fleetingly narrow, implying that much of the collapseproceeds non-self-similarly. We show that our solutions can naturallyincorporate turbulent pressure support, and we investigate the evolution ofoverdensities -- potentially generated by such turbulence -- as the collapseproceeds. Finally, we analyze the evolution of the angular velocity andmagnetic fields in the limit that their dynamical influence is small, and werecover exact solutions for these quantities. Our results may provide importantconstraints on numerical models that attempt to elucidate the details ofprotostellar collapse when the initial conditions are far less idealized.

Spherically-symmetric, cold collapse: the exact solutions and a comparison with self-similar solutions