Geodesic stability, Lyapunov exponents, and quasinormal modes

By V. Cardoso, A. S. Miranda, Emanuele Berti, Helvi Witek, V. Zanchin. 2008

752 citations recorded by the source corpus.

Geodesic motion determines important features of spacetimes. Null unstable geodesics are closely related to the appearance of compact objects to external observers and have been associated with the characteristic modes of black holes. By computing the Lyapunov exponent, which is the inverse of the instability time scale associated with this geodesic motion, we show that, in the eikonal limit, quasinormal modes of black holes in any dimensions are determined by the parameters of the circular null geodesics. This result is independent of the field equations and only assumes a stationary, spherically symmetric and asymptotically flat line element, but it does not seem to be easily extendable to anti-de Sitter spacetimes. We further show that (i) in spacetime dimensions greater than four, equatorial circular timelike geodesics in a Myers-Perry black-hole background are unstable, and (ii) the instability time scale of equatorial null geodesics in Myers-Perry spacetimes has a local minimum for spacetimes of dimension d ≥ 6.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/6cd1966222aeb6dbf4e96855f5e4993a9712e89a

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Citations in the corpus

Superradiance: Energy Extraction, Black-Hole Bombs and Implications for Astrophysics and Particle Physics (2015, background): “Because the potential necessarily develops a local minimum, it is possible to show that in the eikonal limit (l 1) the spectrum contains long-lived modes whose damping time grows exponentially with l [558, 559, 384].”
Superradiance (2015, background): “Because the potential necessarily develops a local minimum, it is possible to show that in the eikonal limit (l 1) the spectrum contains long-lived modes whose damping time grows exponentially with l [819, 820, 555].”
Black Hole Parameter Estimation from Its Shadow (2018, background): “…unstable circular orbits due to the strong gravitational field of the black hole, and these orbits have a very important influence on quasinormal modes (Cardoso et al. 2009; Hod 2009; Konoplya & Stuchlik 2017), gravitational lensing (Stefanov et al. 2010), and the black hole shadow (Bardeen 1973).”
Tests for the existence of black holes through gravitational wave echoes (2017, background): “[8] Cardoso, V and Miranda, AS and Berti, E and Witek, H and Zanchin, VT, Geodesic stability, Lyapunov exponents and quasinormal modes.”