Schwarzschild-de Sitter spacetime: The role of temperature in the emission of Hawking radiation

We consider a Schwarzschild-de Sitter (SdS) black hole, and focus on the emission of massless scalar fields either minimally or non-minimally coupled to gravity. We use six different temperatures, two black-hole and four effective ones for the SdS spacetime, as the question of the proper temperature for such a background is still debated in the literature. We study their profiles under the variation of the cosmological constant, and derive the corresponding Hawking radiation spectra. We demonstrate that only few of these temperatures may support significant emission of radiation. We finally compute the total emissivities for each temperature, and show that the non-minimal coupling constant of the scalar field to gravity also affects the relative magnitudes of the energy emission rates.