Instability of the massive Klein-Gordon field on the Kerr spacetime
By Sam R. Dolan. 2007
374 citations recorded by the source corpus.
We investigate the instability of the massive scalar field in the vicinity of a rotating black hole. The instability arises from amplification caused by the classical superradiance effect. The instability affects bound states: solutions to the massive Klein-Gordon equation which tend to zero at infinity. We calculate the spectrum of bound state frequencies on the Kerr background using a continued-fraction method, adapted from studies of quasinormal modes. We demonstrate that the instability is most significant for the l=1, m=1 state, for M{mu} < or approx. 0.5. For a fast rotating hole (a=0.99) we find a maximum growth rate of {tau}{sup -1}{approx_equal}1.5x10{sup -7}(GM/c{sup 3}){sup -1}, at M{mu}{approx_equal}0.42. The physical implications are discussed.
Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/58bf8d470fcc36f5488bbbc7e158a47bcb739b8d
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Citations in the corpus
- Black holes with only one Killing field (2011, background): “This is reminiscent of what happens in the case of a massive scalar field in the background of the asymptotically flat Kerr black hole [19]-[23].”
- Numerical methods for finding stationary gravitational solutions (2015, background): “Dirichlet walls can be provided by a reflecting box [421–440], by a massive scalar or Proca field potential well [34, 73, 294, 419, 429, 441–448], or by the AdS boundary with reflecting boundary conditions [38–41, 44, 226, 279, 396, 449, 450].”
- Thermodynamics of Rotating Black Holes and Black Rings: Phase Transitions and Thermodynamic Volume (2014, background): “19 Interestingly, they also occur for the massive scalar field in the asymptotically flat d = 4 Kerr black hole spacetime [134, 135].”
- Superradiance (2015, methodology): “The spectrum of massive scalar perturbations of the Kerr metric contains both stable QNMs and quasibound states, which are localized near the BH [446, 447, 105].”
- Superradiance: Energy Extraction, Black-Hole Bombs and Implications for Astrophysics and Particle Physics (2015, methodology): “For a BH with mass M , the shortest instability time scale is τ ∼ ( M 106M ) yr for a ultralight scalar [279, 343, 10, 100, 11], and shorter for vector [10, 99, 100] and tensor fields [11] for which superradiance is more efficient (cf.”
- Constraining the mass of dark photons and axion-like particles through black-hole superradiance (2018, background): “Detailed calculations for the instability rate for scalar fields was done in [33, 34] and highly accurate numerical results will be given in section 2.”
- Probing ultralight bosons with binary black holes (2018, background): “t the horizon. This is encapsulated in the imaginary part of the eigenfrequency, !n‘m!!n‘m+ i n‘m; (2.11) which was omitted in (2.8). In general, the instability rate has to be determined numerically [95]. However, in the limit ˝1, the decay width can be computed analytically. The result, known as ‘”
- The spectra of gravitational atoms (2019, methodology): “Identical results apply to the recursion relation used in [8].”