Perturbations of plane waves and quadratic quasinormal modes on the lightring
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1.
California Institute of Technology
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2.
University of Copenhagen
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3.
Johns Hopkins University
Abstract
We study second order gravitational perturbations on plane wave spacetimes from both the metric and curvature perturbation points of view. For the former, we explicitly use the isometries of the background to introduce tensor oscillator harmonics, which render Einstein’s equations algebraic around symmetric plane waves. For the latter, we formulate the first and second order Teukolsky equations in a Geroch-Held-Penrose covariant way. Both approaches are useful in their own right, and together with our discussion on gauge freedom, they provide a foundation for the study of higher-order gravitational dynamics around plane wave spacetimes. Taking the perspective that these plane wave spacetimes arise from Penrose limits, we subsequently use these results to explore the nonlinear gravitational dynamics close to black hole lightrings. Specifically, we define and discuss quadratic quasinormal mode ratios, observe that they satisfy emergent selection rules, and make publicly available a code to compute them.
Copyright and License
© 2025, The Author(s). Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Acknowledgement
We acknowledge support by VILLUM Foundation (grant no. VIL37766) and the DNRF Chair program (grant no. DNRF162) by the Danish National Research Foundation. The Center of Gravity is a Center of Excellence funded by the Danish National Research Foundation under grant No. 184. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101007855 and No 101131233. K. F. is supported by the Heising-Simons Foundation “Observational Signatures of Quantum Gravity” collaboration grant 2021-2817, the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and the Walter Burke Institute for Theoretical Physics. D. P. is supported by NSF Grants No. AST-2307146, PHY-2513337, PHY-090003, and PHY-20043, by NASA Grant No. 21-ATP21-0010, by John Templeton Foundation Grant No. 62840, by the Simons Foundation, and by Italian Ministry of Foreign Affairs and International Cooperation Grant No. PGR01167.
Files
JHEP12(2025)148.pdf
Additional details
Related works
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- Discussion Paper: arXiv:2509.03598 (arXiv)
Funding
- Villum Fonden
- VIL37766
- Danish National Research Foundation
- DNRF162
- Danish National Research Foundation
- 184
- European Commission
- 101007855
- European Commission
- 101131233
- Heising-Simons Foundation
- 2021-2817
- United States Department of Energy
- DE-SC0011632
- National Science Foundation
- AST-2307146
- National Science Foundation
- PHY-2513337
- National Science Foundation
- PHY-090003
- National Science Foundation
- PHY-20043
- National Aeronautics and Space Administration
- 21-ATP21-0010
- John Templeton Foundation
- 62840
- Italian Ministry of Foreign Affairs and International Cooperation
- PGR01167
Caltech Custom Metadata
- Caltech groups
- Division of Physics, Mathematics and Astronomy (PMA) , Walter Burke Institute for Theoretical Physics
- Publication Status
- Published