Interpolating the stretched dS2 horizon Sample Clauses

Interpolating the stretched dS2 horizon. ‌ We end this section by considering the interpolating solution for ϕ˜ < 0 in some more de- tail. For the purpose of our discussion, it will prove useful to slightly generalise the dilaton potential (1.37) to the following δ δ V (ϕ) = 2ϕ −Θ(−ϕ) + 1 Θ(ϕ) + ϕ˜, (1.54) with ϕ˜ < 0, and δ a small positive number. In order to have an interpolating solution with an asymptotic AdS2 region, the horizon rh must lie below the critical value rδ ≡ ϕ˜(1+√1 + δ )/2. At precisely rh = rδ the geometry caps off for a second time at r = −ϕ˜δ/2, creating a closed Euclidean universe. If we now tune rh to be parametrically close to and below rδ and take ϕb ≫ 1, we find an asymptotically near-AdS2 geometry which includes a significant portion of the two-sphere. The interpolating saddle stemming from Vδ(ϕ) admits a portion of the two-sphere for which
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