Annales Henri Poincaré

, Volume 11, Issue 5, pp 805–880 | Cite as

Improved Decay for Solutions to the Linear Wave Equation on a Schwarzschild Black Hole

  • Jonathan Luk


We prove that sufficiently regular solutions to the wave equation \({\square_g\phi=0}\) on the exterior of the Schwarzschild black hole obey the estimates \({|\phi|\leq C_\delta v_+^{-\frac{3}{2}+\delta}}\) and \({|\partial_t\phi|\leq C_{\delta} v_+^{-2+\delta}}\) on a compact region of r, including inside the black hole region. 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.


Black Hole Event Horizon Minkowski Spacetime Linear Wave Decay Estimate 
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Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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