Kerr spacetime In terms of Boyer-Lindquist coordinates,7,0,the metric of a Kerr spacetime is de(12Cia +(+2GM327sin20. sinGMasind where △=P-2GM+a2,∑=2+a2cos20, and a is the Kerr parameter a=J/M. For a near extreme Kerr BH,introduce a parameter <<1. The ISCO and IBCO have different scaling behaviors under A-0 limit GM+21/3,23GM+0A) GM+21/2λGM+o(). This motivates us to consider two different limits of near horizon geometry. 口卡三4色至习Q0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kerr spacetime In terms of Boyer-Lindquist coordinates ˆt,ˆr, θ, ϕˆ, the metric of a Kerr spacetime is ds2 = −(1 − 2GMˆr Σ )dˆt + Σ ∆ dˆr 2 + Σdθ 2 + +(ˆr 2 + a 2 + 2GMa2ˆrsin2 θ Σ )sin2 θdϕˆ2 − 4GMaˆrsin2 θ Σ dˆtdϕˆ where ∆ ≡ ˆr 2 − 2GMˆr + a 2 , Σ ≡ ˆr 2 + a 2 cos2 θ, and a is the Kerr parameter a = J/M. For a near extreme Kerr BH, introduce a parameter λ = √ 1 − J 2 M4 << 1. The ISCO and IBCO have different scaling behaviors under λ → 0 limit ˆrISCO = GM + 21/3λ 2/3GM + O(λ) ˆrIBCO = GM + 21/2λGM + o(λ). This motivates us to consider two different limits of near horizon geometry