Effective Temperatures and Radiation Spectra for a Higher-Dimensional
  Schwarzschild-de-Sitter Black-Hole
  The absence of a true thermodynamical equilibrium for an observer located in
the causal area of a Schwarzschild-de Sitter spacetime has repeatedly raised
the question of the correct definition of its temperature. In this work, we
consider five different temperatures for a higher-dimensional Schwarzschild-de
Sitter black hole: the bare $T_0$, the normalised $T_{BH}$ and three effective
ones given in terms of both the black hole and cosmological horizon
temperatures. We find that these five temperatures exhibit similarities but
also significant differences in their behaviour as the number of extra
dimensions and the value of the cosmological constant are varied. We then
investigate their effect on the energy emission spectra of Hawking radiation.
We demonstrate that the radiation spectra for the normalised temperature
$T_{BH}$ -- proposed by Bousso and Hawking over twenty years ago -- leads to
the dominant emission curve while the other temperatures either support a
significant emission rate only at a specific $\Lambda$ regime or they have
their emission rates globally suppressed. Finally, we compute the
bulk-over-brane emissivity ratio and show that the use of different
temperatures may lead to different conclusions regarding the brane or bulk
dominance.
