Summary: In a recent paper, M.K.-H. Kiessling and A.S. Tahvildar-Zadeh [Indiana Univ. Math. J. 57, No. 7, 3177–3208 (2008; Zbl 1173.35008)] proved that any classical solution of the relativistic Vlasov-Poisson equation with attractive coupling launched by spherically symmetric initial data with unit mass, zero total energy, and virial less than or equal to -1/2 will blow up in finite time. They left open whether such data exist. Subsequently, the question was raised whether any such data exist at all. In fact, the simplest conceivable ansatz, a nearly uniform ball of material centered at the origin with momenta directed inward, must have virial strictly larger than -1/2! In this paper, we settle this issue by constructing two classes of such initial data. {
©2011 American Institute of Physics}