Near-NHEK:very near horizon region We may take a different limit:入-→0，fixed t二 2MK -i4,重=6-2 t we will find the near-NHEK geometry:L Bredbers etal.0907.3 ds2 =2MPT(0) dr2 r+2xue+2四+d+Aoo++a9） where >0 is arbitrary as a consequence of emerging scale invariance. The near-NHEK is closer to the horizon than the NHEK.It has enhanced SL(2,R)U(1)symmetry as well. Besides the enhanced symmetry,there is a discrete PT-symmetry in both NHEK and near-NHEK geometries: T→-T,Φ-ΦNHEK t→-t,p→-near-NHEK 口卡+·三4色，在习80. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Near-NHEK: very near horizon region We may take a different limit: λ → 0, κ fixed t = ˆt 2Mκ λ, r = κ ˆr −ˆr+ Mλ , Φ = ϕˆ − ˆt 2M , we will find the near-NHEK geometry: I. Bredberg et.al. 0907.3477 ds2 = 2M2Γ(θ) ( −r(r + 2κ)dt2 + dr2 r(r + 2κ) + dθ 2 + Λ2 (θ)(dϕ + (r + κ)dt) 2 ) , where κ > 0 is arbitrary as a consequence of emerging scale invariance. The near-NHEK is closer to the horizon than the NHEK. It has enhanced SL(2, R) × U(1) symmetry as well. Besides the enhanced symmetry, there is a discrete PT-symmetry in both NHEK and near-NHEK geometries: T → −T, Φ → −Φ NHEK t → −t, ϕ → −ϕ near-NHEK