Inserting tanh((r-r_h)/delta) into the inverse radial BTZ metric produces a black bounce whose throat sits exactly at an extremal null horizon, with no Lorentzian-to-Riemannian signature change.
The (t,z ) sector has constant curvature −λ2/2: the near-throat geometry is AdS2 ×S1, ℓ AdS2 = √ 2δ/F ′(rh), (15) the standard near-horizon geometry of a degenerate horizon
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A smooth BTZ black bounce with an extremal null throat
Inserting tanh((r-r_h)/delta) into the inverse radial BTZ metric produces a black bounce whose throat sits exactly at an extremal null horizon, with no Lorentzian-to-Riemannian signature change.