Perturbations of slowly rotating black holes: massive vector fields in the Kerr metric
By Paolo Pani, V. Cardoso, L. Gualtieri, Emanuele Berti, A. Ishibashi. 2012
158 citations recorded by the source corpus.
We discuss a general method to study linear perturbations of slowly rotating black holes which is valid for any perturbation field, and particularly advantageous when the field equations are not separable. As an illustration of the method we investigate massive vector (Proca) perturbations in the Kerr metric, which do not appear to be separable in the standard Teukolsky formalism. Working in a perturbative scheme, we discuss two important effects induced by rotation: a Zeeman-like shift of nonaxisymmetric quasinormal modes and bound states with different azimuthal number m, and the coupling between axial and polar modes with different multipolar index l. We explicitly compute the perturbation equations up to second order in rotation, but in principle the method can be extended to any order. Working at first order in rotation we show that polar and axial Proca modes can be computed by solving two decoupled sets of equations, and we derive a single master equation describing axial perturbations of spin s=0 and s=+-1. By extending the calculation to second order we can study the superradiant regime of Proca perturbations in a self-consistent way. For the first time we show that Proca fields around Kerr black holes exhibit a superradiant instability, which is significantly stronger than for massive scalar fields. Because of this instability, astrophysical observations of spinning black holes provide the tightest upper limit on the mass of the photon: mv<4x10^-20 eV under our most conservative assumptions. Spin measurements for the largest black holes could reduce this bound to mv<10^-22 eV or lower.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/7dad03b47fd57d2340a95cd42a82a0c6634bbffb
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Citations in the corpus
- Probing ultralight bosons with binary black holes (2018, background): “(9)See [97,98] which point out a missing factor of 1=2 in Detweiler’s original computation.”
- Holographic thermalization, quasinormal modes and superradiance in Kerr-AdS (2013, background): “To get this result, as observed in a similar context in [100], we should keep in mind that the angular eigenvalue is an integer strictly only in the limit of zero rotation.”
- 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, background): “2 and are in good agreement with the analytical results, the latter are available only for the Proca axial modes [99].”
- The spectra of gravitational atoms (2019, methodology): “Unfortunately, these equations are not yet known, except at linear order in ã [20, 21].”
- Constraining the mass of dark photons and axion-like particles through black-hole superradiance (2018, methodology): “[15, 45, 46], and it was observed that the instability timescales could be substantially shorter [15, 45] than for scalars (thus potentially improving constraints on ULVs).”
- 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].”