Near-Nariai with a boundary Sample Clauses

Near-Nariai with a boundary. ‌ In order to compute the thermal partition function, we place a boundary at some value r = rb ∈ (rh, −rh), where ϕb = rb and βT are fixed. The boundary can either surround the black hole or cosmological horizon. In fact, there is no choice of saddle here. Rather, all saddles must be included provided they satisfy the same Dirichlet boundary conditions. However, of all the saddles, one will generally dominate. Thus, we must evaluate the thermodynamic quantities for both horizons in the presence T h b of a boundary at rb. For the black hole horizon at r = rh, the analysis of the previous section can be directly applied, resulting in log Z bh = 2π(ϕ 0 h + r ) + β qr2 − ϕ2 , r 2π ϕ | |b h 4π2 − β2 = − √
Sample 1
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