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

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 a yet different method to look at the problem. In the case of a Schwarzschild black hole it is known that this methods affirms the existence of a black hole remnant (minimal mass $M_{\min }$) of the order of Planck mass $m_{\mathrm{pl}}$ and a corresponding maximal temperature $T_{\max }$ also of the order of $m_{\mathrm{pl}}$. The standard $T(M)$ dispersion relation is, in the GUP formulation, deformed in the vicinity of Planck length $l_{\mathrm{pl}}$ 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 $(m_{\mathrm{pl}}/m_{\Lambda })m_{\mathrm{pl}}$, minimum temperature $T_{\min }\sim m_{\Lambda }$. As compared to the standard approach we find a deformed dispersion relation $T(M)$ close to $l_{\mathrm{pl}}$ and in addition at the maximally possible horizon approximately at $r_{\Lambda }=1/m_{\Lambda }$. $T(M)$ agrees with the standard results at $l_{\mathrm{pl}}\ll r\ll r_{\Lambda }$ (or equivalently at $M_{\min }\ll M\ll M_{\max }$).

new references added

References in corpus (20)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Extra force in $f(R)$ modified theories of gravity
• The Generalized Uncertainty Principle in (A)dS Space and the Modification of Hawking Temperature from the Minimal Length
• Cosmological expansion and local physics
• Natural extension of the Generalised Uncertainty Principle
• Black hole thermodynamics with generalized uncertainty principle
• Influence of Generalized and Extended Uncertainty Principle on Thermodynamics of FRW universe
• On the influence of the cosmological constant on gravitational lensing in small systems
• Quantum Mechanics and the Generalized Uncertainty Principle
• Thermodynamics of a black hole based on a generalized uncertainty principle
• Generalized Uncertainty Principle, Modified Dispersion Relations and Early Universe Thermodynamics
• Entropy and temperature of black holes in a gravity's rainbow
• Does the cosmological constant imply the existence of a minimum mass?
• Canonical entropy of three-dimensional BTZ black hole
• Entropy of a charged black hole in two dimensions without cutoff
• A revision of the Generalized Uncertainty Principle
• Ellipsoidal configurations in the de Sitter spacetime
• From Global to Local Dynamics: Effects of the Expansion on Astrophysical Structures
• Dangerous implications of a minimum length in quantum gravity
• Dark Energy in an Astrophysical Context

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• Extended GUP formulation and the role of momentum cut-off
• Maximal extension of the Schwarzschild spacetime inspired by noncommutative geometry
• On the Black Holes in alternative theories of gravity: The case of non-linear massive gravity
• Influence of GUP corrected Casimir energy on zero tidal force wormholes in modified teleparallel gravity with matter coupling
• The Komar mass function in the de-Rham-Gabadadze-Tolley non-linear theory of massive gravity
• The Astrophysical Scales Set by the Cosmological Constant, Black-Hole Thermodynamics and Non-Linear Massive Gravity
• Regular black holes with $\Lambda >0$ and its evolution in Lovelock gravity
• Perturbing microscopic black holes inspired by noncommutativity
• On a model of magnetically charged black hole with nonlinear electrodynamics
• GUP-Corrected van der Waals Black Holes
• Microstructure and Continuous Phase Transition of the Gauss-Bonnet AdS Black Hole
• Entropy of higher-dimensional topological dS black holes with nonlinear source
• Minimal-length quantum field theory: a first-principle approach
• Hawking radiation and thermodynamics of dynamical black holes in phantom dominated universe
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