Quasinormal modes of black holes and black branes

Abstract

Abstract. 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.

Sources of Gravitational Waves: Theory and Observations

“…A binary's GW luminosity reaches its peak soon after it reaches the LSO. The merged object in all cases, except for very low total-mass NS binaries, is a highly deformed BH that quickly settles down to a quiescent Kerr state, emitting a characteristic spectrum of damped sinusoidal GWs -the quasinormal modes (QNMs) [301]. The complex frequencies of the QNMs depend on the mass and spin of the final BH.…”

“…Following the closelimit result [276], in a first approximation the plunge and QNM signals are matched at the light ring (i.e., at the unstable photon circular orbit), where the peak of the potential barrier around the newborn BH is located. Thus, the EOB merger-ringdown waveform is built as a linear superposition of QNMs of the final Kerr BH [66,281] h merger-RD 20) where N is the number of overtones [282,283], A mn is the complex amplitude of the n-th overtone, and σ mn = ω mn − i/τ mn is the complex frequency of this overtone with positive (real) frequency ω mn and decay time τ mn . The complex QNM frequencies are known functions of the mass and spin of the final Kerr BH.…”

Holographic collisions in confining theories

“…This method is an extension of a Frobenius expansion used originally in refs. [48][49][50] (see also ref. [44] for a review).…”

On the Kerr-AdS/CFT correspondence

“…It serves as a mock-up model of true interactions in large-N N = 4 SYM and some deformations of it [2,3], like N = 2 SYM with generic matter multiplets in the adjoint and/or fundamental. In general relativity, it also tests linear stability of solutions [4], relaxation times [5], as well as relation with the Conformal Field Theory (CFT) bootstrap, represented by Liouville field theory [6]. Most of the applications, however, either focus on low dimension, with the Bañados-Teitelboim-Zanelli (BTZ) black hole [7] serving as a ubiquitous background, or on higher-dimensional solutions without rotation -a serious drawback for many interesting physical phenomena, like superradiance, the zero temperature moduli and the fate of the inner horizon.…”