0 Ju n 20 09 Improved decay for solutions to the linear wave equation on a Schwarzschild black hole

@inproceedings{Luk20090JN,
  title={0 Ju n 20 09 Improved decay for solutions to the linear wave equation on a Schwarzschild black hole},
  author={Jonathan Winghong Luk},
  year={2009}
}
We prove that sufficiently regular solutions to the wave equation gφ = 0 on the exterior of the Schwarzschild black hole obey the estimates |φ| ≤ Cδv − 3 2 +δ + and |∂tφ| ≤ Cδv −2+δ + on a compact region of r and along the event horizon. This is proved with the help of a new vector field commutator that is analogous to the scaling vector field on Minkowski spacetime. This result improves the known decay rates in the region of finite r and along the event horizon.