Existence of Steady States of the Massless Einstein–Vlasov System Surrounding a Schwarzschild Black Hole

Abstract We show that there exist steady states of the spherically symmetric massless Einstein–Vlasov system which surround a Schwarzschild black hole. The are (thick) shells with finite mass and compact support. Furthermore we prove an arbitrary number shells, necessarily well separated, can To our knowledge this is first result static self-gravitating solutions to any Einstein-matter also include numerical investigation about properties shells.