Comparing two approaches to Hawking radiation of Schwarzschild-de Sitter black holes

We study two different ways to analyze the Hawking evaporation of a Schwarzschild-de Sitter black hole. The first one uses the standard approach of surface gravity evaluated at the possible horizons. The second method derives its results via the generalized uncertainty principle (GUP) which offers yet a different method to look at the problem. In the case of a Schwarzschild black hole it is known that this method affirms the existence of a black hole remnant (minimal mass M-min) of the order of Planck mass m(pl) and a corresponding maximal temperature T-max also of the order of m(pl). The standard T (M) dispersion relation is, in the GUP formulation, deformed in the vicinity of Planck length l(pl) which is the smallest value the horizon can take. We generalize the uncertainty principle to Schwarzschild-de Sitter spacetime with the cosmological constant Lambda = 1/m(Lambda)(2) and find a dual relation which, compared to M-min and T-max, affirms the existence of a maximal mass M-max of the order (m(pl)/m(Lambda))m(pl), minimum temperature T-min similar to m(Lambda). As compared to the standard approach we find a deformed dispersion relation T(M) close to l(pl) and in addition at the maximally possible horizon approximately at r(Lambda) = 1/m(Lambda). T (M) agrees with the standard results at l(pl) << r << r(Lambda) (or equivalently at M-min << M << M-max).