Static spherically symmetric Einstein-Vlasov shells made up of particles with a discrete set of values of their angular momentum

In this paper we study static spherically symmetric Einstein-Vlasov shells, made up of equal mass particles, where the angular momentum L of particles takes values only on a discrete finite set. We consider first the case where there is only one value of L, and prove their existence by constructing explicit examples. Shells with either hollow or black hole interiors have finite thickness. Of particular interest is the thin shell limit of these systems, and we study its properties using both numerical and analytic arguments to compare with known results. The general case of a set of values of L is also considered and the particular case where L takes only two values is analyzed, and compared with the corresponding thin shell limit already given in the literature, finding good agreement in all cases.