## Abstract

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 Λ = 1/m^{2}_{Λ} 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_{Λ})m _{pl}, minimum temperature T_{min} ∼ m_{Λ}. 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_{Λ} = 1/m_{Λ}. T(M) agrees with the standard results at l_{pl} ≪ r ≪ r_{Λ} (or equivalently at M_{min} ≪ M ≪ M_{max}).

Original language | British English |
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Article number | 125006 |

Journal | Classical and Quantum Gravity |

Volume | 26 |

Issue number | 12 |

DOIs | |

State | Published - 2009 |