No-go theorem for false vacuum black holes

We study the possibility of non-singular black hole solutions in the theory of general relativity coupled to a nonlinear scalar:field with a positive potential possessing two minima: a 'false vacuum' with;positive energy and a 'true vacuum' with zero energy. Assuming that the scalar field starts 'at the false vacuum at the origin and comes to the true vacuum at spatial inf inity, we prove a no-go theorem by extending a no-hair theorem to the black hole interior: no smooth solutions exist which interpolate between the loc al de Sitter solution near the origin and the asymptotic Schwarzschild solu tion through a regular event horizon or several horizons.