Type-II Weyl semimetal vs gravastar

Abstract: The boundary between the type I and type II Weyl semimetals serves as the event horizon for the "relativistic" fermions. The interior of the black hole is represented by the type II Weyl semimetal, where the Fermi surface is formed. The process of the filling of the Fermi surface by electrons results in the relaxation inside the horizon. This leads to the Hawking radiation and to the reconstruction of the interior vacuum state. After the Fermi surface is fully occupied, the interior region reaches the equilibrium state, for which the Hawking radiation is absent. If this scenario is applicable to the real black hole, then the final state of the black hole will be the dark energy star with the event horizon. Inside the event horizon one would have de Sitter space time, which is separated from the event horizon by the shell of the Planck length width. Both the de Sitter part and the shell are made of the vacuum fields without matter. This is distinct from the gravastar, in which the matter shell is outside the "horizon", and which we call the type I gravastar. But this is similar to the other type of the vacuum black hole, where the shell is inside the event horizon, and which we call the type II gravastar. We suggest to study the vacuum structure of the type II gravastar using the $q$-theory, where the vacuum variable is the 4-form field introduced for the phenomenological description of the quantum vacuum.