The perturbation theory of higher dimensional spacetimes a la Teukolsky

Abstract

We consider the possibility of deriving a decoupled equation in terms of Weyl tensor components for gravitational perturbations of the Schwarzschild-Tangherlini solution. We find a particular gauge invariant component of the Weyl tensor does decouple and argue that this corresponds to the vector modes of Ishibashi and Kodama. Also, we construct a Hertz potential map for solutions of the electromagnetic and gravitational perturbation equations of a higher dimensional Kundt background using the decoupled equation of Durkee and Reall. Motivated by recent work of Guica and Strominger, we use this to construct the asymptotic behaviour of metric perturbations of the near-horizon geometry of the 5d cohomogeneity-1 Myers-Perry black hole.

References in corpus (10)

• Black holes in three dimensional higher spin gravity: A review
• Instability and new phases of higher-dimensional rotating black holes
• No Dynamics in the Extremal Kerr Throat
• Bar-mode instability of rapidly spinning black hole in higher dimensions: Numerical simulation in general relativity
• Generalization of the Geroch-Held-Penrose formalism to higher dimensions
• Ultraspinning instability of rotating black holes
• Nonaxisymmetric instability of rapidly rotating black hole in five dimensions
• Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes
• Linearized gravity and gauge conditions
• Algebraically special axisymmetric solutions of the higher-dimensional vacuum Einstein equation

Cited by in corpus (10)

• Algebraic classification of higher dimensional spacetimes based on null alignment
• Quasinormal modes of asymptotically flat rotating black holes
• Kerr-AdS and its Near-horizon Geometry: Perturbations and the Kerr/CFT Correspondence
• Petrov Type, Principal Null Directions, and Killing Tensors of Slowly-Rotating Black Holes in Quadratic Gravity
• Spinor-helicity and the algebraic classification of higher-dimensional spacetimes
• Instabilities of extremal rotating black holes in higher dimensions
• Scaling and Universality in Extremal Black Hole Perturbations
• Near Horizon Extremal Geometry Perturbations: Dynamical Field Perturbations vs. Parametric Variations
• Spin coefficients and gauge fixing in the Newman-Penrose formalism
• Generalized wave operators, weighted Killing fields, and perturbations of higher dimensional spacetimes