Recently, it was found that the energy flux of a free scalar quantum field on
a Reissner-Nordstr\"om-de Sitter spacetime has a quadratic divergence towards
the inner horizon of the black hole. Moreover, the leading divergence was found
to be state independent as long as the spectral gap of the wave equation on the
spacetime is sufficiently large. In this work, we show that the latter result
can be extended to all subextremal Reissner-Nordstr\"om-de Sitter and
subextremal Kerr-de Sitter spacetimes with a positive spectral gap.Comment: 24 pages, 4 figure