Stability of the evaporating Schwarzschild-de Sitter black hole final state

Time-independent backreaction corrections of the renormalized expectation value of the stress tensor operator of a massless quantum scalar field, coupled in a two-dimensional spherically symmetric Schwarzschild-de Sitter static black hole metric, are used to obtain its final state. According to the work by Christensen and Fulling, the renormalized stress tensor is found to be determined by the nonlocal contribution of the trace anomaly and some additional parameters. Mathematical derivations of the backreaction equations, in close relation to the work by Bousso and Hawking, show that the scenario of the black hole Hawking radiation is reduced to a remnant, stable, static, Schwarzschild-de Sitter mini black hole which has still new black hole and cosmological shrunk horizons