Improved decay rates with small regularity loss for the wave equation about a Schwarzschild black hole

@inproceedings{Blue2008ImprovedDR,
  title={Improved decay rates with small regularity loss for the wave equation about a Schwarzschild black hole},
  author={Pieter Blue and Abner Soffer},
  year={2008}
}
We continue our study of the decoupled wave equation in the exterior of a spherically symmetric, Schwarzschild, black hole. Because null geodesics on the photon sphere orbit the black hole, extra effort must be made to show that the high angular momentum components of a solution decay sufficiently fast, particularly for low regularity initial data. Previous results are rapid decay for regular (H 3 ) initial data [6] and slower decay for rough (H 1+ǫ ) initial data [5]. Here, we combine those… CONTINUE READING

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