Hidden symmetries and decay for the wave equation on the Kerr spacetime

By Lars-Erik Andersson, P. Blue. 2009

189 citations recorded by the source corpus.

Energy and decay estimates for the wave equation on the exterior region of slowly rotating Kerr spacetimes are proved. The method used is a generalisation of the vector-field method that allows the use of higher-order symmetry operators. In particular, our method makes use of the second-order Carter operator, which is a hidden symmetry in the sense that it does not correspond to a Killing symmetry of the spacetime.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/00091e06fb0c89ba938d2e0e01919931cc573400

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In Mathematical Physics

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Citations in the corpus

Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case |a| < M (2014, methodology): “wever, there does not exist a unique high frequency limit of rmax, consistent with the fact [2] that these currents cannot be replaced by a classical vector ﬁeld deﬁned in physical space. See however [3]. At the level of geodesic ﬂow, this precisely reﬂects the fact that trapped null geodesics exist”
The global non-linear stability of the Kerr-de Sitter family of black holes (2016, background): “Apart from [37], bundle-valued (or coupled systems of) equations were studied in particular in the contexts of Maxwell’s equations by Andersson and Blue [15], [4], [5] and Sterbenz–Tataru [130] (see also [84], [50]), and for Dirac equations by Finster, Kamran, Smoller and Yau [58].”
The linear stability of the Schwarzschild solution to gravitational perturbations (2016, background): “The analogous construction cannot, however, be done by a traditional vector field current; see [24, 1, 70] for the |a| ≪ M case and [26] for the full |a| < M case, where in addition to the hyperbolicity of trapping, the fact that trapped frequencies are not superradiant also plays an important role.”