Black hole and cosmos with multiple horizons and multiple singularities in vector-tensor theories.

A stationary and spherically symmetric black hole (For example, Reissner-Nordstr$\ddot{\textrm{o}}$m black hole or Kerr-Newman black hole) has at most one singularity and two horizons. One horizon is the outer event horizon and the other is the inner Cauchy horizon. Can we construct static and spherically symmetric black hole solutions with $N$ horizons and $M$ singularities? De Sitter cosmos has only one apparent horizon. Can we construct cosmos solutions with $N$ horizons? In this article, we present the static and spherically symmetric black hole and cosmos solutions with $N$ horizons and $M$ singularities in the vector-tensor theories. Following these motivations, we also construct the black hole solutions with a firewall. The deviation of these black hole solutions from the usual ones can be potentially tested by future measurements of gravitational waves.