2014/12/16 by Dejan Gajic, Gajic, Dejan
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Advanced Mathematical Physics Problems
paper · pdf · doi:10.48550/arxiv.1412.5190
In this paper we consider the Klein-Gordon equation on spherically symmetric\nbackground spacetimes with a constant area radius. The spacetimes under\nconsideration are Nariai and Pleba 'nski-Hacyan, and can be considered constant\nradius limits of Reissner-Nordstr "om-de Sitter spacetimes. We prove\nboundedness in the case of a non-negative Klein Gordon mass and decay unless\nthe mass is zero. In the latter case we prove decay of solutions that are\nsupported on all harmonic modes with angular momentum l greater or equal to 1.\nWe show that the l=0 modes of solutions to the massless Klein-Gordon equation\ndo not decay. They are subject to conservation laws along degenerate Killing\nhorizons. We apply the estimates in Nariai to give decay of solutions to the\nmassive Klein-Gordon equation on an n-dimensional de Sitter background, using\nonly the vector field method and with no restrictions on the positive\nKlein-Gordon mass.\n