Existence of steady states of the massless Einstein-Vlasov system surrounding a Schwarzschild black hole

Understand

We show that there exist steady states of the massless Einstein-Vlasov system which surround a Schwarzschild black hole.

• The steady states are (thick) shells with finite mass and compact support.
• Furthermore we prove that an arbitrary number of shells, necessarily well separated, can surround the black hole.
• To our knowledge this is the first result of static self-gravitating solutions to any massless Einstein-matter system which surround a black hole.