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In a recent paper, Kiessling and Tahvildar-Zadeh proved that any classicalsolution of the relativistic Vlasov-Poisson equation with attractive couplinglaunched by spherically symmetric initial data with zero total energy andvirial less than or equal to -1/2 will blow up in finite time. They left openwhether such data exist. Subsequently, the question was raised whether any suchdata exist at all. In fact, the simplest conceivable ansatz, a nearly uniformball of material centered at the origin with momenta directed inward, must havevirial strictly larger than -1/2! In this brief note, we settle this issue byconstructing two classes of such initial data.

journal of mathematical physics

Existence of Spherical Initial Data with Unit Mass, Zero Energy, and  Virial less than - 1/2 for the Relativistic Vlasov-Poisson Equation with  Attractive Coupling