AUTHOR=Panosso Macedo Rodrigo , Zenginoğlu Anıl 

TITLE=Hyperboloidal approach to quasinormal modes

JOURNAL=Frontiers in Physics

VOLUME=Volume 12 - 2024

YEAR=2025

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2024.1497601

DOI=10.3389/fphy.2024.1497601

ISSN=2296-424X

ABSTRACT=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.