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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
Article

Abstract

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.

Keywords

Black Hole Event Horizon Minkowski Spacetime Linear Wave Decay Estimate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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