Dynamics of Extremal Black Holes by Stefanos Aretakis

Author:Stefanos Aretakis
Language: eng
Format: epub, pdf
ISBN: 9783319951836
Publisher: Springer International Publishing

2.3.6 Asymptotics for Type B Perturbations

Perturbations of Type B satisfy and and hence represent local perturbations from afar. In the physics literature, such perturbations represent ingoing radiation.

Recall that Lucietti–Murata–Reall–Tanahashi [13] numerically demonstrated that such perturbations exhibit a weaker version of the horizon instability (see Sect. 2.3.2), namely

(2.3.12)

Perturbations of Type B which exhibit the above behavior where rigorously constructed in [31]. However, [31] did not provide a necessary and sufficient condition for perturbations of Type B so that (2.3.12) holds. Such a condition and moreover the precise late-time asymptotics for all perturbations of Type B were obtained in [28].

Recall that the horizon charge given by (2.3.6) is well-defined for all Type B perturbations. It turns out that the weak horizon instability (2.3.12) holds if and only if . Specifically,

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