Regular black hole remnants in de Sitter space

We address the question of thermodynamical evolution of regular spherically symmetric cosmological black holes with de Sitter center. Space–time is asymptotically de Sitter as r→0r→0 and as r→∞r→∞. A source term in the Einstein equations connects smoothly two de Sitter vacua with different values of cosmological constant and corresponds to anisotropic vacuum dark fluid defined by symmetry of its stress–energy tensor. In the range of masses Mcr1⩽M⩽Mcr2Mcr1⩽M⩽Mcr2 it describes a regular cosmological black hole with three horizons, an internal horizon rara, a black hole horizon rb>rarb>ra, and a cosmological horizon rc>rbrc>rb. Thermodynamical preference for a final product of evaporation is a double-horizon (ra=rbra=rb) black hole remnant with the positive specific heat.