Can an evolving Universe host a static event horizon?

Abstract

We prove the existence of general relativistic perfect fluid black hole solutions, and demonstrate the phenomenon for the $P=w\rho$ class of equations of state. While admitting a local time-like Killing vector on the event horizon itself, the various black hole configurations are necessarily time dependent (thereby avoiding a well known no-go theorem) away from the horizon. Consistently, Hawking's imaginary time periodicity is globally manifest on the entire spacetime manifold.