The belief still persists, at least for an important part of the community, that in general relativity the cosmological constant Lambda must remain immaculate. However, Bianchi identities show that Lambda could acquire local properties in the presence of matter, i.e., Lambda -> Lambda(x(mu)). In this paper we go even further, and we show that a non-uniform vacuum energy does not even require coexistence with any additional form of matter-energy, nor of any theory beyond general relativity, at least for extreme environments, such as the proximity of a black hole.