English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the Cauchy problem for the wave equation in a general class ofspherically symmetric black hole geometries. Under certain mild conditions onthe far-field decay and the singularity, we show that there is a uniqueglobally smooth solution to the Cauchy problem for the wave equation with datacompactly supported away from the horizon that is compactly supported for alltimes and \emph{decays in $L^{\infty}_{\text{loc}}$ as $t$ tends to infinity}.We obtain as a corollary that in the geometry of black hole solutions of theSU(2) Einstein/Yang-Mills equations, solutions to the wave equation withcompactly supported initial data decay as $t$ goes to infinity.

The Wave Equation in a General Spherically Symmetric Black Hole Geometry