2014/01/02 by Parul Laul, Jason Metcalfe, Laul, Parul +5
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Advanced Mathematical Physics Problems #Cosmology and Gravitation Theories
paper · pdf · doi:10.48550/arxiv.1401.0465
Localized energy estimates for the wave equation have been increasingly used to prove various other dispersive estimates. This article focuses on proving such localized energy estimates on (1+4)-dimensional Myers-Perry black hole backgrounds with small angular momenta. The Myers-Perry space-times are generalizations of higher dimensional Kerr backgrounds where additional planes of rotation are availabile while still maintaining axial symmetry. Once it is determined that all trapped geodesics have constant r, the method developed by Tataru and the fourth author, which perturbs off of the Schwarzschild case by using a pseudodifferential multiplier, can be adapted.