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October 2010 Stability and decay rates for the five-dimensional Schwarzschild metric under biaxial perturbations
Gustav Holzegel
Adv. Theor. Math. Phys. 14(5): 1245-1372 (October 2010).

Abstract

In this paper we prove the non-linear asymptotic stability of the five-dimensional Schwarzschild metric under biaxial vacuum perturbations. This is the statement that the evolution of $(SU (2) \times (U(1))$)-symmetric vacuum perturbations of initial data for the five-dimensional Schwarzschild metric finally converges in a suitable sense to a member of the Schwarzschild family. It constitutes the first result proving the existence of non-stationary vacuum black holes arising from asymptotically flat initial data dynamically approaching a stationary solution. In fact, we show quantitative rates of approach. The proof relies on vectorfield multiplier estimates, which are used in conjunction with a bootstrap argument to establish polynomial decay rates for the radiation on the perturbed spacetime. Despite being applied here in a five-dimensional context, the techniques are quite robust and may admit applications to various four-dimensional stability problems.

Citation

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Gustav Holzegel. "Stability and decay rates for the five-dimensional Schwarzschild metric under biaxial perturbations." Adv. Theor. Math. Phys. 14 (5) 1245 - 1372, October 2010.

Information

Published: October 2010
First available in Project Euclid: 21 September 2011

zbMATH: 1243.83023
MathSciNet: MR2826184

Rights: Copyright © 2010 International Press of Boston

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Vol.14 • No. 5 • October 2010
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