A pseudospectrum analysis has recently provided evidence of a potential generic instability of black hole (BH) quasinormal mode (QNM) overtones under high-frequency perturbations. Such instability analysis depends on the assessment of the size of perturbations. This is encoded in the scalar product and its choice is not unique. We address the impact of the scalar product choice, founding it on the physical energy scales of the problem. The article is organized in three parts: basics, applications and heuristic proposals. In the first part, we revisit the energy scalar product used in the hyperboloidal approach to QNMs, extending previous effective analyses and placing them on solid spacetime basis. The second part focuses on applications of the scalar product in the QNM problem: i) we demonstrate that the QNM instability is not an artifact of previous spectral numerical schemes, by implementing a finite elements calculation from a weak formulation; ii) using Keldysh's theorem, we provide QNM resonant expansions for the gravitational waveform, with explicit expressions of the expansion coefficients; iii) we propose the notion of "epsilon-dual QNM expansions" to exploit BH QNM instability in BH spectroscopy, exploiting both non-perturbed and perturbed QNMs, the former informing on large scales and the latter probing small scales. The third part enlarges the conceptual scope of BH QNM instability proposing: a) spiked perturbations are more efficient in triggering BH QNM instabilities than smooth ones, b) a general picture of the BH QNM instability problem is given, supporting the conjecture (built on Burnett's conjecture) that Nollert-Price branches converge universally to logarithmic Regge branches in the high-frequency limit and c) aiming at a fully geometric description of QNMs, BMS states are hinted as possible asymptotic/boundary degrees of freedom for an inverse scattering problem.
Living on the Edge of Effective Field Theory: Near-Extremal Black Holes in Quadratic Gravity
Illinois Center for Advanced Studies of the Universe & Department of Physics, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校物理系及宇宙高级研究中心）；Department of Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校物理系）
Analyzing Quasi-normal modes spectrum in asymptotically de Sitter black bounces and their optical appearance
Universidade Federal do Ceará (UFC)（塞阿拉联邦大学）；University of Valladolid UVA（巴利亚多利德大学）；Universidad del Bío-Bío（比奥比奥大学）；Research Centre for Theoretical Physics and Astrophysics, Institute of Physics, Silesian University in Opava（俄帕瓦西里西亚大学物理研究所理论物理与天体物理研究中心）
A new rotating axionic AdS$_4$ black hole dressed with a scalar field
Universidad Católica del Maule（天主教马乌莱大学）；Damghan University（达姆甘大学）；Universidade Federal do Maranhão（马拉尼昂联邦大学）；Universidad Nacional Autónoma de Honduras（洪都拉斯国立自治大学）；Benemérita Universidad Autónoma de Puebla（普埃布拉自治优秀大学）；Universidad de Antioquia（安蒂奥基亚大学）
