Stability and decay-rates for the five-dimensional Schwarzschild metric under biaxial perturbations - General Relativity and Quantum CosmologyReport as inadecuate




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Abstract: In this paper we prove the non-linear asymptotic stability of thefive-dimensional Schwarzschild metric under biaxial vacuum perturbations.
Thisis the statement that the evolution of SU2 x U1-symmetric vacuumperturbations of initial data for the five-dimensional Schwarzschild metricfinally converges in a suitable sense to a member of the Schwarzschild family.It constitutes the first result proving the existence of non-stationary vacuumblack holes arising from asymptotically flat initial data dynamicallyapproaching a stationary solution.
In fact, we show quantitative rates ofapproach.
The proof relies on vectorfield multiplier estimates, which are usedin conjunction with a bootstrap argument to establish polynomial decay ratesfor the radiation on the perturbed spacetime.
Despite being applied here in afive-dimensional context, the techniques are quite robust and may admitapplications to various four-dimensional stability problems.



Author: G.
Holzegel


Source: https://arxiv.org/



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