Alternatively, it was suggested in [73, 71] that one can describe the dynamics of the scalar field in the near-horizon region using the truncated expansion of Δr (r) around r+ at second order. However, the resulting function trunc Δ r has, in addition to the pole r+, a fake pole r∗, which is not associated with any geometric or thermodynamic feature of the solution. Therefore, the physical meaning of this truncation is unclear.