Quasinormal Modes Beyond Kerr

The quasinormal modes (QNMs) of a black hole spacetime are the free, decaying oscillations of the spacetime, and are well understood in the case of Kerr black holes. We discuss a method for computing the QNMs of spacetimes which are slightly deformed from Kerr. We mention two example applications: the parametric, turbulent instability of scalar fields on a background which includes a gravitational QNM, and the shifts to the QNM frequencies of Kerr when the black hole is weakly charged. This method may be of use in studies of black holes which are deformed by external fields or are solutions to alternative theories of gravity.Comment: Proceedings of the Sant Cugat Forum on Astrophysics (2014). Session on 'Gravitational Wave Astrophysics.' 7 page

Relativistic Perturbation Theory for Black-Hole Boson Clouds

We develop a relativistic perturbation theory for scalar clouds around rotating black holes. We first introduce a relativistic product and corresponding orthogonality relation between modes, extending a recent result for gravitational perturbations. We then derive the analog of time-dependent perturbation theory in quantum mechanics, and apply it to calculate self-gravitational frequency shifts. This approach supersedes the nonrelativistic “gravitational atom” approximation, brings close agreement with numerical relativity, and has practical applications for gravitational-wave astronomy

Pseudospectrum of horizonless compact objects: a bootstrap instability mechanism

Recent investigations of the pseudospectrum in black hole spacetimes have shown that quasinormal mode frequencies suffer from spectral instabilities. This phenomenon may severely affect gravitational-wave spectroscopy and limit precision tests of general relativity. We extend the pseudospectrum analysis to horizonless exotic compact objects which possess a reflective surface arbitrarily close to the Schwarzschild radius, and find that their quasinormal modes also suffer from an overall spectral instability. Even though all the modes themselves decay monotonically, the pseudospectrum contours of equal resonance magnitude around the fundamental mode and the lowest overtones can cross the real axis into the unstable regime of the complex plane, unveiling the existence of nonmodal pseudo-resonances. A pseudospectrum analysis further predicts that fluctuations to the system may destabilize the object when next to leading-order effects are considered, as the triggering of pseudo-resonant growth can break the order-expansion of black-hole perturbation theory.Comment: 19 pages, 5 figures; v2: minor changes and references adde

An approach to computing spectral shifts for black holes beyond Kerr

Recent measurements of gravitational-wave ringdown following the merger of binary black holes raise the prospect of precision black hole spectroscopy in the near future. To perform the most sensitive tests of the nature of black holes using ringdown measurements, it is critical to compute the deviations to the spectrum of black holes in particular extensions of relativity. These spectral shifts are also needed to interpret any violations of the predictions of relativity that may be detected during ringdown. Here we present a first step towards computing the shifts to the spectrum of Kerr black holes with arbitrary spins, by deriving a modified Teukolsky equation governing the perturbations of black holes in theories beyond GR. Our approach applies to a class of theories which includes dynamical Chern-Simons gravity and shift-symmetric scalar Gauss-Bonnet gravity, in the case where the deviations from relativity are small. This allows for a perturbative approach to solving the equations of motion. Further, we show how to use the modified equation to compute the leading-order spectral shifts of Kerr black holes, using eigenvalue perturbation methods. Our formalism provides a practical approach to predicting ringdown for black holes in a range of promising extensions to relativity, enabling future precision searches for their signatures in black hole ringdown.Comment: 23 pages, 1 figur

Damped and zero-damped quasinormal modes of charged, nearly extremal black holes

Despite recent progress, the complete understanding of the perturbations of charged, rotating black holes as described by the Kerr-Newman metric remains an open and fundamental problem in relativity. In this study, we explore the existence of families of quasinormal modes of Kerr-Newman black holes whose decay rates limit to zero at extremality, called zero-damped modes in past studies. We review the nearly extremal and WKB approximation methods for spin-weighted scalar fields (governed by the Dudley-Finley equation) and give an accounting of the regimes where scalar zero-damped and damped modes exist. Using Leaver’s continued fraction method, we verify that these approximations give accurate predictions for the frequencies in their regimes of validity. In the nonrotating limit, we argue that gravito-electromagnetic perturbations of nearly extremal Reissner-Nordström black holes have zero-damped modes in addition to the well-known spectrum of damped modes. We provide an analytic formula for the frequencies of these modes, verify their existence using a numerical search, and demonstrate the accuracy of our formula. These results, along with recent numerical studies, point to the existence of a simple universal equation for the frequencies of zero-damped gravito-electromagnetic modes of Kerr-Newman black holes, whose precise form remains an open question

The universal Teukolsky equations and black hole perturbations in higher-derivative gravity

We reduce the study of perturbations of rotating black holes in higher-derivative extensions of general relativity to a system of decoupled radial equations that stem from a set of universal Teukolsky equations. We detail a complete computational strategy to obtain these decoupled equations in general higher-derivative theories. We apply this to six-derivative gravity to compute the shifts in the quasinormal mode frequencies with respect to those of Kerr black holes in general relativity. At linear order in the angular momentum we reproduce earlier results obtained with a metric perturbation approach. In contrast with this earlier work, however, the method given here applies also to post-merger black holes with significant spin, which are of particular observational interest.Comment: 50 pages, 5 figures. v2: we fixed an error in our code and this led to improved results for the QNMs reported in section 6. The rest of the sections remain unchanged up to small adjustements. Conclusions unchanged. Version sent to the journal. We provide an ancillary Mathematica notebook with the modified Teukolsky radial equations for the (l,m)=(2,3) and (3,3) modes in six-derivative gravit

Black-hole spectroscopy: quasinormal modes, ringdown stability and the pseudospectrum

Black-hole spectroscopy is a powerful tool to probe the Kerr nature of astrophysical compact objects and their environment. The observation of multiple ringdown modes in gravitational waveforms could soon lead to high-precision gravitational-wave spectroscopy, thus it is critical to understand if the quasinormal mode spectrum itself is affected by astrophysical environments, quantum corrections, and other generic modifications. In this chapter, we will review the black-hole spectroscopy program and its challenges regarding quasinormal mode detection, the overtone status and the recent evidence that supports the existence of nonlinearities in the spectrum of black holes. We will then discuss a newly introduced non-modal tool in black-hole physics, namely the pseudospectrum; a mathematical notion that can shed light on the spectral stability of quasinormal modes, and discuss its novel applications in black holes and exotic horizonless compact objects. We will show that quasinormal modes generically suffer from spectral instabilities, explore how such phenomena can further affect black-hole spectroscopy, and discuss potential ringdown imprints and waveform stability issues in current and future gravitational-wave detectors.Comment: 35 pages, 24 figures, Topical review presented on the 11th Aegean Summer School, Syros, Greece, References adde