The Null Condition and Global Existence for Nonlinear Wave Equations on Slowly Rotating Kerr Spacetimes

Details The Null Condition and Global Existence for Nonlinear Wave Equations on Slowly Rotating Kerr Spacetimes The Null Condition and Global Existence for Nonlinear Wave Equations on Slowly Rotating Kerr Spacetimes

2010-09-21

arxiv.org/abs/1009.4109v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in time and decays with a quantitative rate to the trivial solution. The proof uses the robust vector field method. It makes use of the decay properties of the linear wave equation on Kerr spacetime, in particular the improved decay rates in the region $\{r\leq \frac{t}{4}\}$.

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