Black hole (BH) oscillations known as quasi-normal modes (QNMs) are one of the most important gravitational wave (GW) sources. We propose that higher perturbative order of QNMs, generated by nonlinear gravitational interaction near the BHs, are detectable and worth searching for in observations and simulations of binary BH mergers. We calculate the metric perturbations to second-order and explicitly regularize the master equation at the horizon and spatial infinity. We find that the second-order QNMs have frequencies twice the first-order ones and the GW amplitude is up to ∼ 10% that of the first-order one. The QNM frequency would also shift blueward up to ∼ 1%. This provides a new test of general relativity as well as a possible distance indicator.

Publication Date



This is the pre-print of an article published by the American Physical Society. The final, published version is available here: https://doi.org/10.1103/PhysRevD.76.061503

© 2007 American Physical Society

Also archived in arXiv:0704.3467 v3 Aug 3, 2007

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type


Department, Program, or Center

School of Physics and Astronomy (COS)


RIT – Main Campus