Quintessence and black holes

We present new static spherically symmetric exact solutions of the Einstein equations for quintessential matter surrounding a black hole, charged or uncharged, as well as for the case without a black hole. A condition of additivity and linearity in the energy–momentum tensor is introduced which allows one to obtain correct limits to known solutions for the electromagnetic static field, implying the relativistic relation between the energy density and pressure, as well as for the extraordinary case of the cosmological constant, i.e. de Sitter space. We classify the horizons, which evidently reveal themselves in static coordinates, and derive the Gibbons–Hawking temperatures. An example of quintessence with state parameter w = −2/3 is discussed in detail.