Master Equations for Perturbations of Generalised Static Black Holes with Charge in Higher Dimensions

By H. Kodama, A. Ishibashi. 2003

297 citations recorded by the source corpus.

We extend the formulation for perturbations of maximally symmetric black holes in higher dimensions developed by the present authors in a previous paper to a charged black hole background whose horizon is described by an Einstein manifold. For charged black holes, perturbations of electromagnetic fields are coupled to the vector and scalar modes of metric perturbations non-trivially. We show that by taking appropriate combinations of gauge-invariant variables for these perturbations, the perturbation equations for the Einstein-Maxwell system are reduced to two decoupled second-order wave equations describing the behaviour of the electromagnetic mode and the gravitational mode, for any value of the cosmological constant. These wave equations are transformed into Schrodinger-type ODEs through a Fourier transformation with respect to time. Using these equations, we investigate the stability of generalised black holes with charge. We also give explicit expressions for the source terms of these master equations with application to the emission problem of gravitational waves in mind.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/753ba77733d8bb7eac72946823ce8a41fb976d29

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Citations in the corpus

Superradiance (2015, background): “]. 2001Emparan and Reall provide the rst example of a stationary asymptotically at vacuum solution with an event horizon of nonspherical topology the \black ring" [80]. 2003In a series of papers [81,82,83], Kodama and Ishibashi extend the Regge-Wheeler-Zerilli formalism to higher dimensions. 20”
Static patch solipsism: conformal symmetry of the de Sitter worldline (2011, unknown): “The resulting Schrödinger potentials, for scalar, vector and tensor modes, respectively, are [38, 39] VS = ( − 1) sinh(2) y − (d − 3)(d − 5) 4 cosh(2) y , (19)”
DE SITTER MUSINGS (2012, unknown): “Similarly, given that the global geometry is contracting if we begin at I−, a large class of data at I− will never (2)Though we do not discuss linearized gravity in a fixed de Sitter background in this article, a very complete discussion can be found in [14, 15].”
Black Holes in Higher Dimensions (2008, methodology): “13Note that this does not disagree with the stability result of [164] for d = 4 Reissner–Nordström-AdS since the instability involves scalar fields and hence cannot be seen within minimal N = 2 gauged supergravity.”
Superradiance: Energy Extraction, Black-Hole Bombs and Implications for Astrophysics and Particle Physics (2015, background): “2003 In a series of papers [86, 87, 88], Kodama and Ishibashi extend the Regge-Wheeler-Zerilli formalism to higher dimensions.”
Overdamped modes in Schwarzschild-de Sitter and a Mathematica package for the numerical computation of quasinormal modes (2017, background): “These are the unique (up to taking linear combinations) gauge invariant combinations of the fluctuations, though if one allows for their radial derivatives as well there are more possibilities [47].”
On the classification of asymptotic quasinormal frequencies for $d$-dimensional black holes and quantum gravity (2004, methodology): “[10] discusses the stability of black holes in asymptotically dS spacetimes to tensor, vector and scalar perturbations.”
Holographic Quantum Matter (2016, unknown): “for a 2+1 dimensional dual field theory) extremal AdS-RN these equations were found and solved in [231; 232; 233], building on [469].”