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

• Published in: Classical and quantum gravity 2009-06, Vol.26 (12), p.125006-125006 (22)
• Main Authors: Arraut, I, Batic, D, Nowakowski, M
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; General relativity and gravitation; Physics
• ISSN: 0264-9381; 1361-6382
• DOI: 10.1088/0264-9381/26/12/125006

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 Mmin) of the order of Planck mass mpl and a corresponding maximal temperature Tmax also of the order of mpl. The standard T(M) dispersion relation is, in the GUP formulation, deformed in the vicinity of Planck length lpl 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/m2 Lambda and find a dual relation which, compared to Mmin and Tmax, affirms the existence of a maximal mass Mmax of the order (mpl/m Lambda )mpl, minimum temperature Tmin ~ m Lambda . As compared to the standard approach we find a deformed dispersion relation T(M) close to lpl and in addition at the maximally possible horizon approximately at r Lambda = 1/m Lambda . T(M) agrees with the standard results at lpl r r Lambda (or equivalently at Mmin M Mmax).