Quasinormal modes of brane-localized standard model fields. II. Kerr black holes (original) (raw)
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Quasinormal modes of brane-localized standard model fields
Physical Review D, 2006
We present here a detailed study of the quasi-normal spectrum of brane-localised Standard Model fields in the vicinity of D-dimensional black-holes. A variety of such backgrounds (Schwarzschild, Reissner-Nordstrom and Schwarzszchild-(Anti) de Sitter) are investigated. The dependence of the quasi-normal spectra on the dimensionality D, spin of the field s, and multipole number l is analyzed. Analytical formulae are obtained for a number of limiting cases: in the limit of large multipole number for Schwarzschild, Schwarzschild-de Sitter and Reissner-Nordstrom black holes, in the extremal limit of the Schwarzschild-de Sitter black hole, and in the limit of small horizon radius in the case of Schwarzschild-Anti de Sitter black holes. We show that an increase in the number of hidden, extra dimensions results in the faster damping of all fields living on the brane, and that the localization of fields on a brane affects the QN spectrum in a number of additional ways, both direct and indirect.
Rotating black holes in brane worlds
Journal of High Energy Physics, 2004
We study interaction of rotating higher dimensional black holes with a brane in space-times with large extra dimensions. In the approximation when a black hole is slowly rotating and the tension of the brane is small we demonstrate that the black hole loses some angular momentum to the brane. As a result of this effect a black hole in its final stationary state can have only those components of the angular momenta which are connected with Killing vectors generating transformations preserving a position of the brane. The characteristic time when a rotating black hole with the gravitational radius r 0 reaches this final state is T ∼ r p−1 0 /(Gσ), where G is the higher dimensional gravitational coupling constant, σ is the brane tension, and p is the number of extra dimensions.
2004
doi:10.1088/0264-9381/21/14/011 We study interaction of rotating higher-dimensional black holes with a brane in spacetimes with large extra dimensions. We demonstrate that in a general case a rotating black hole attached to a brane can lose bulk components of its angular momenta. A stationary black hole can have only those components of the angular momenta which are connected with Killing vectors generating transformations preserving a position of the brane. In a final stationary state the null Killing vector generating the black hole horizon is tangent to the brane. We discuss first the interaction of a cosmic string and a domain wall with the 4D Kerr black hole. We then prove the general result for slowly rotating higher-dimensional black holes interacting with branes. The characteristic time when a rotating black hole with gravitational radius r0 reaches this final stationary state is T ∼ rp−10 /(Gσ), where G is the higher-dimensional gravitational coupling constant, σ is the bra...
Interaction of higher-dimensional rotating black holes with branes
Classical and Quantum Gravity, 2004
We study interaction of rotating higher dimensional black holes with a brane in space-times with large extra dimensions. We demonstrate that in a general case a rotating black hole attached to a brane can loose bulk components of its angular momenta. A stationary black hole can have only those components of the angular momenta which are connected with Killing vectors generating transformations preserving a position of the brane. In a final stationary state the null Killing vector generating the black hole horizon is tangent to the brane. We discuss first the interaction of a cosmic string and a domain wall with the 4D Kerr black hole. We then prove the general result for slowly rotating higher dimensional black holes interacting with branes. The characteristic time when a rotating black hole with the gravitational radius r 0 reaches this final stationary state is T ∼ r p−1 0 /(Gσ), where G is the higher dimensional gravitational coupling constant, σ is the brane tension, and p is the number of extra dimensions.
TOPICAL REVIEW: Quasinormal modes of black holes and black branes
Classical and Quantum Gravity, 2009
Quasinormal modes are eigenmodes of dissipative systems. Perturbations of classical gravitational backgrounds involving black holes or branes naturally lead to quasinormal modes. The analysis and classification of the quasinormal spectra requires solving non-Hermitian eigenvalue problems for the associated linear differential equations. Within the recently developed gauge-gravity duality, these modes serve as an important tool for determining the near-equilibrium properties of strongly coupled quantum field theories, in particular their transport coefficients, such as viscosity, conductivity and diffusion constants. In astrophysics, the detection of quasinormal modes in gravitational wave experiments would allow precise measurements of the mass and spin of black holes as well as new tests of general relativity. This review is meant as an introduction to the subject, with a focus on the recent developments in the field.
Stability of five-dimensional rotating black holes projected on the brane
2003
We study the stability of five-dimensional Myers-Perry black holes with a single angular momentum under linear perturbations, and we compute the quasinormal modes (QNM's) of the black hole metric projected on the brane, using Leaver's continued fraction method. In our numerical search we do not find unstable modes. The damping time of modes having l = m = 2 and l = m = 1 tends to infinity as the black hole spin tends to the extremal value, showing a behaviour reminiscent of the one observed for ordinary 4-dimensional Kerr black holes.
Highly damped quasinormal modes of Kerr black holes
Physical Review D, 2003
Motivated by recent suggestions that highly damped black hole quasinormal modes (QNM's) may provide a link between classical general relativity and quantum gravity, we present an extensive computation of highly damped QNM's of Kerr black holes. We do not limit our attention to gravitational modes, thus filling some gaps in the existing literature. The frequency of gravitational modes with l=m=2 tends to \omega_R=2 \Omega, \Omega being the angular velocity of the black hole horizon. If Hod's conjecture is valid, this asymptotic behaviour is related to reversible black hole transformations. Other highly damped modes with m>0 that we computed do not show a similar behaviour. The real part of modes with l=2 and m<0 seems to asymptotically approach a constant value \omega_R\simeq -m\varpi, \varpi\simeq 0.12 being (almost) independent of a. For any perturbing field, trajectories in the complex plane of QNM's with m=0 show a spiralling behaviour, similar to the one observed for Reissner-Nordstrom (RN) black holes. Finally, for any perturbing field, the asymptotic separation in the imaginary part of consecutive modes with m>0 is given by 2\pi T_H (T_H being the black hole temperature). We conjecture that for all values of l and m>0 there is an infinity of modes tending to the critical frequency for superradiance (\omega_R=m) in the extremal limit. Finally, we study in some detail modes branching off the so--called ``algebraically special frequency'' of Schwarzschild black holes. For the first time we find numerically that QNM multiplets emerge from the algebraically special Schwarzschild modes, confirming a recent speculation.
Numerical study of the quasinormal mode excitation of Kerr black holes
Physical Review D, 2006
We present numerical results from three-dimensional evolutions of scalar perturbations of Kerr black holes. Our simulations make use of a high-order accurate multi-block code which naturally allows for fixed adaptivity and smooth inner (excision) and outer boundaries. We focus on the quasinormal ringing phase, presenting a systematic method for extraction of the quasinormal mode frequencies and amplitudes and comparing our results against perturbation theory.
Perturbations of slowly rotating black holes: Massive vector fields in the Kerr metric
Physical Review D, 2012
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 Zeemanlike 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: mγ 4 × 10 −20 eV under our most conservative assumptions. Spin measurements for the largest black holes could reduce this bound to mγ 10 −22 eV or lower.
Constraining extra dimensions using observations of black hole quasi-normal modes
2021
The presence of extra dimensions generically modify the spacetime geometry of a rotating black hole, by adding an additional hair, besides the mass M and the angular momentum J , known as the ‘tidal charge’ parameter, β. In a braneworld scenario with one extra spatial dimension, the extra dimension is expected to manifest itself through — (a) negative values of β, and (b) modified gravitational perturbations. This in turn would affect the quasi-normal modes of rotating black holes. We numerically solve the perturbed gravitational field equations using the continued fractions method and determine the quasi-normal mode spectra for the braneworld black hole. We find that increasingly negative values of β correspond to a diminishing imaginary part of the quasinormal mode, or equivalently, an increasing damping time. Using the publicly available data of the properties of the remnant black hole in the gravitational wave signal GW150914, we check for consistency between the predicted value...