Cosmological perturbations in the Regge-Wheeler formalism

We study linear perturbations of the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model in the Regge-Wheeler formalism which is a standard framework to study perturbations of spherically-symmetric black holes. In particular, we show that the general solution of linear perturbation equations can be given in terms of two copies of a master scalar satisfying scalar wave equation on the FLRW background (with a Regge-Wheeler/Zerilli type potential) thus representing two gravitational degrees of freedom, and one scalar satisfying a transport type equation representing (conformal) matter perturbation. We expect the Regge-Wheeler formalism to be easily extended to include nonlinear perturbations, akin to to the recent work [Phys. Rev. D 96, 124026 (2017)].Comment: 5 pages, no figure

Comment on "AdS nonlinear instability: moving beyond spherical symmetry" [Class. Quantum Grav. 33 23LT01 (2016)]

We argue that if the degeneracy of the spectrum of linear perturbations of AdS is properly taken into account, there are globally regular, time-periodic, asymptotically AdS solutions (geons) bifurcating from each linear eigenfrequency of AdS.Comment: 1 page, v2: missing $\theta$ dependence in eqs. (3,4) adde

Towards a theory of nonlinear gravitational waves: a systematic approach to nonlinear gravitational perturbations in vacuum

We present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, we show that the system of perturbative Einstein equations reduces at each perturbation order to two (for each gravitational mode in 3 + 1 dimensions on which our study is focused) scalar wave equations, and then we show how the metric perturbations can be explicitly obtained, once the solutions to these scalar wave equations are known. These results show that the concept of polarization of a gravitational wave does make sense also beyond the linear approximation.Comment: 14 pages. arXiv admin note: text overlap with arXiv:1701.07804; v2: 16 pages, minor changes in the text, misprint in Eqs. (39,62,63,67,68) corrected, Eq. (70) added, 5 references adde

Lecture Notes on Turbulent Instability of Anti-de Sitter Spacetime

In these lecture notes we discuss recently conjectured instability of anti-de Sitter space, resulting in gravitational collapse of a large class of arbitrarily small initial perturbations. We uncover the technical details used in the numerical study of spherically symmetric Einstein-massless scalar field system with negative cosmological constant that led to the conjectured instability.Comment: Lecture notes from the NRHEP spring school held at IST-Lisbon, March 2013. To be published by IJMPA (V. Cardoso, L. Gualtieri, C. Herdeiro and U. Sperhake, Eds., 2013); v2: sec. 6 and acknowledgments added, matches published versio

What drives AdS unstable?

We calculate the spectrum of linear perturbations of standing wave solutions discussed in [Phys. Rev. D 87, 123006 (2013)], as the first step to investigate the stability of globally regular, asymptotically AdS, time-periodic solutions discovered in [Phys. Rev. Lett. 111 051102 (2013)]. We show that while this spectrum is only asymptotically nondispersive (as contrasted with the pure AdS case), putting a small standing wave solution on the top of AdS solution indeed prevents the turbulent instability. Thus we support the idea advocated in previous works that nondispersive character of the spectrum of linear perturbations of AdS space is crucial for the conjectured turbulent instability.Comment: 7 pages, 4 figures; v2: minor corrections in the tex

Gravitational turbulent instability of AdS5{}_5

We consider the problem of stability of anti-de Sitter spacetime in five dimensions under small purely gravitational perturbations satisfying the cohomogeneity-two biaxial Bianchi IX ansatz. In analogy to spherically symmetric scalar perturbations, we observe numerically a black hole formation on the time-scale $\mathcal{O}(\varepsilon^{-2})$, where $\varepsilon$ is the size of the perturbation.Comment: talk given at Strings2014, Princeton, June 201

Comment on "Holographic Thermalization, stability of AdS, and the Fermi-Pasta-Ulam-Tsingou paradox" by V. Balasubramanian et al

We comment upon a numerical computation in a recent paper by Balasubramanian, Buchel, Green, Lehner, and Liebling.Comment: 1 pag