Master equations and stability of Einstein-Maxwell-scalar black holes

Abstract

We derive master equations for linear perturbations in Einstein-Maxwell-scalar theory, for any spacetime dimension D and any background with a maximally symmetric n = (D - 2)-dimensional spatial component. This is done by expressing all fluctuations analytically in terms of several master scalars. The resulting master equations are Klein-Gordon equations, with non-derivative couplings given by a potential matrix of size 3, 2 and 1 for the scalar, vector and tensor sectors respectively. Furthermore, these potential matrices turn out to be symmetric, and positivity of the eigenvalues is sufficient (though not necessary) for linear stability of the background under consideration. In general these equations cannot be fully decoupled, only in specific cases such as Reissner-Nordström, where we reproduce the Kodama-Ishibashi master equations. Finally we use this to prove stability in the vector sector of the GMGHS black hole and of Einstein-scalar theories in general.

arXiv commenttypos fixed (we thank Alex Buchel for pointing them out), results made available as Mathematica notebooks on www.github.com/APJansen/MasterEquations

References in corpus (26)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Supersymmetry and Quantum Mechanics
• Quasinormal modes of black holes and black branes
• Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium
• Quasinormal modes and holography
• A master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions
• Quasi-Normal Modes of Schwarzschild Anti-De Sitter Black Holes: Electromagnetic and Gravitational Perturbations
• Master equations for perturbations of generalised static black holes with charge in higher dimensions
• Mimicking the QCD equation of state with a dual black hole
• Stability of Higher-Dimensional Schwarzschild Black Holes
• Black Holes as Elementary Particles
• Holography and Thermodynamics of 5D Dilaton-gravity
• Gauge-invariant gravitational perturbations of maximally symmetric spacetimes
• Instability and new phases of higher-dimensional rotating black holes
• Black holes and black branes in Lifshitz spacetimes
• Linear stability of Einstein-Gauss-Bonnet static spacetimes. Part II: vector and scalar perturbations
• Linear stability of Einstein-Gauss-Bonnet static spacetimes. Part I: tensor perturbations
• Master Equations for Gravitational Perturbations of Static Lovelock Black Holes in Higher Dimensions
• Quasinormal modes and the phase structure of strongly coupled matter
• Quasinormal modes of weakly charged Einstein-Maxwell-dilaton black holes
• Gauge Invariant Perturbations of the Schwarzschild Spacetime
• Towards a theory of nonlinear gravitational waves: a systematic approach to nonlinear gravitational perturbations in vacuum
• Stability analysis of black holes by the $S$-deformation method for coupled systems
• Cosmological perturbations in the Regge-Wheeler formalism
• EZ gauge is singular at the event horizon
• Nonlinear perturbations of Reissner-Nordström black holes

Cited by in corpus (13)

• Complexified quasinormal modes and the pole-skipping in a holographic system at finite chemical potential
• Quasinormal modes in charged fluids at complex momentum
• Dynamically and thermodynamically stable black holes in Einstein-Maxwell-dilaton gravity
• Critical behaviour of hydrodynamic series
• Thermodynamically stable asymptotically flat hairy black holes with a dilaton potential: the general case
• Entropy production from quasinormal modes
• Bulk Spacetime Encoding via Boundary Ambiguities
• The Algebraic Structure Underlying Pole-Skipping Points
• Black hole spectroscopy and nonlinear echoes in Einstein-Maxwell-scalar theory
• Stabilization of the extended horizons
• Master equations for de Sitter DFPs
• Spectral Problems for Quasinormal Modes of Black Holes
• Diffusion and instabilities in large-N holographic Fermi liquids: the vector fluctuations of the electron star