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arXiv · 1909.06733

The linear stability of the Schwarzschild spacetime in the harmonic gauge: even part

Pei-Ken Hung
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Abstract

In this paper we study the even part of the linear stability of the Schwarzschild spacetime as a continuation of [22]. By taking the harmonic gauge, we prove that the energy decays at a rate $\tau^{-2+}$ for the solution of the linearized Einstein equation after subtracting its spherically symmetric part. We further show that the spherically symmetric part converges to a linear combination of two special solutions. One is the gauge-fixed mass change solution [19]. The other is the deformation tensor of a stationary one form, which solves the tensorial wave equation. As a key ingredient, we prove that the solutions of the tensorial wave equation converge to this stationary one form up to a scalar multiplication.

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Pei-Ken Hung. 2019-09-15. The linear stability of the Schwarzschild spacetime in the harmonic gauge: even part. https://arxiv.org/abs/1909.06733

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