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

Understand

In this paper, we study the odd solution of the linearlized Einstein equation on the Schwarzschild background and in the harmonic gauge.

• With the aid of Regge-Wheeler quantities, we are able to estimate the odd part of Lichnerowicz d'Alembertian equation.
• In particular, we prove the solution decays at rate $\tau^{-1+\delta}$ to a linearlized Kerr solution.