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MINI REVIEW article

Front. Phys.
Sec. Interdisciplinary Physics
Volume 12 - 2024 | doi: 10.3389/fphy.2024.1497601
This article is part of the Research Topic Quasi-Normal Modes, Non-Selfadjoint Operators and Pseudospectrum: an Interdisciplinary Approach View all 11 articles

Hyperboloidal Approach to Quasinormal Modes

Provisionally accepted
Rodrigo Panosso Macedo Rodrigo Panosso Macedo 1*Anil Zenginoglu Anil Zenginoglu 2
  • 1 Niels Bohr Institute, Faculty of Natural and Life Sciences, University of Copenhagen, Copenhagen, Denmark
  • 2 Institute for Physical Science and Technology, College of Computer, Mathematical and Natural Sciences, University of Maryland, College Park, College Park, Maryland, United States

The final, formatted version of the article will be published soon.

    Oscillations of black hole spacetimes exhibit divergent behavior near the bifurcation sphere and spatial infinity. In contrast, these oscillations remain regular when evaluated near the event horizon and null infinity. The hyperboloidal approach provides a natural framework to bridge these regions smoothly, resulting in a geometric regularization of time-harmonic oscillations, known as quasinormal modes (QNMs). This review traces the development of the hyperboloidal approach to QNMs in asymptotically flat spacetimes, emphasizing both the physical motivation and recent advancements in the field. By providing a geometric perspective, the hyperboloidal approach offers an elegant framework for understanding black hole oscillations, with implications for improving numerical simulations, stability analysis, and the interpretation of gravitational wave signals.

    Keywords: Hyperboloidal, frequency domain, Quasinormal modes, black holes, non-selfadjoint operators

    Received: 17 Sep 2024; Accepted: 12 Dec 2024.

    Copyright: © 2024 Panosso Macedo and Zenginoglu. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Rodrigo Panosso Macedo, Niels Bohr Institute, Faculty of Natural and Life Sciences, University of Copenhagen, Copenhagen, Denmark

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