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- W2103137044 abstract "We compute the quantum string entropy S s (m, H) from the microscopic string density of states ρ s (m, H) of mass m in Anti-de Sitter space–time. For high m, (high Hm → c/α′), no phase transition occurs at the Anti-de Sitter string temperature T s = (1/2πk B )L cl c 2 /α′, which is higher than the flat space (Hagedorn) temperature t s . (L cl = c/H, the Hubble constant H acts as producing a smaller string constant α′ and thus, a higher tension). T s is the precise quantum dual of the semiclassical (QFT) Anti-de Sitter temperature scale T sem = ℏc/(2πk B L cl ). We compute the quantum string emission σ string by a black hole in Anti-de Sitter (or asymptotically Anti-de Sitter) space–time (bhAdS). For T sem bhAdS ≪ T s (early evaporation stage), it shows the QFT Hawking emission with temperature T sem bhAdS (semiclassical regime). For T sem bhAdS → T s , it exhibits a phase transition into a Anti-de Sitter string state of size [Formula: see text], and Anti-de Sitter string temperature T s . New string bounds on the black hole emerge in the bhAdS string regime. The bhAdS string regime determines a maximal value for H : H max = 0.841c/l s . The minimal black hole radius in Anti-de Sitter space–time turns out to be r g min = 0.841l s , and is larger than the minimal black hole radius in de Sitter space–time by a numerical factor equal to 2.304. We find a new formula for the full AdS entropy S sem (H), as a function of the usual Bekenstein–Hawking entropy [Formula: see text]. For L cl ≫ ℓ Planck , i.e. for low H ≪ c/ℓ Planck , or classical regime, [Formula: see text] is the leading term with its logarithmic correction, but for high H ≥ c/ℓ Planck or quantum regime, no phase transition operates, in contrast to de Sitter space, and the entropy S sem (H) is very different from the Bekenstein–Hawking term [Formula: see text]." @default.
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- W2103137044 date "2007-03-20" @default.
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- W2103137044 title "SEMICLASSICAL (QFT) AND QUANTUM (STRING) ANTI-DE SITTER REGIMES: NEW RESULTS" @default.
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- W2103137044 doi "https://doi.org/10.1142/s0217751x07035008" @default.
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