Analysis of linear waves near the Cauchy horizon of cosmological black holes

摘要: We show that linear scalar waves are bounded and continuous up to the Cauchy horizon of Reissner-Nordstrom-de Sitter Kerr-de spacetimes, in fact decay exponentially fast a constant along horizon. obtain our results by modifying spacetime beyond suitable manner, which puts wave equation into framework number standard as well more recent microlocal regularity scattering theory apply. In particular, conormal at - yields boundedness statement is consequence radial point estimates, manifestations blue-shift red-shift effects.