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Article Dans Une Revue International Journal of Modern Physics A Année : 2007

Semiclassical (qft) and Quantum (string) Anti-De Sitter Regimes:. New Results

Résumé

We compute the quantum string entropy Ss(m, H) from the microscopic string density of states rhos(m, H) of mass m in Anti-de Sitter space-time. For high m, (high Hm --> c/alpha'), no phase transition occurs at the Anti-de Sitter string temperature Ts = (1/2pikB)Lclc2/alpha', which is higher than the flat space (Hagedorn) temperature ts. (Lcl = c/H, the Hubble constant H acts as producing a smaller string constant alpha' and thus, a higher tension). Ts is the precise quantum dual of the semiclassical (QFT) Anti-de Sitter temperature scale Tsem = ℏc/(2pikBLcl). We compute the quantum string emission sigmastring by a black hole in Anti-de Sitter (or asymptotically Anti-de Sitter) space-time (bhAdS). For Tsem bhAdS ≪ Ts (early evaporation stage), it shows the QFT Hawking emission with temperature Tsem bhAdS (semiclassical regime). For Tsem bhAdS --> Ts, it exhibits a phase transition into a Anti-de Sitter string state of size Ls = ls2/L_ cl, (ls = &surd; hbar alpha '/c}), and Anti-de Sitter string temperature Ts. New string bounds on the black hole emerge in the bhAdS string regime. The bhAdS string regime determines a maximal value for H : Hmax = 0.841c/ls. The minimal black hole radius in Anti-de Sitter space-time turns out to be rg min = 0.841ls, 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 Ssem(H), as a function of the usual Bekenstein-Hawking entropy S sem(0)(H). For Lcl ≫ lPlanck, i.e. for low H ≪ c/lPlanck, or classical regime, S sem(0)(H) is the leading term with its logarithmic correction, but for high H >= c/lPlanck or quantum regime, no phase transition operates, in contrast to de Sitter space, and the entropy Ssem(H) is very different from the Bekenstein-Hawking term S sem(0)(H).

Dates et versions

hal-03742312 , version 1 (02-08-2022)

Identifiants

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A. Bouchareb, Marina Ramón Medrano, Norma G. Sánchez. Semiclassical (qft) and Quantum (string) Anti-De Sitter Regimes:. New Results. International Journal of Modern Physics A, 2007, 22, pp.1395-1416. ⟨10.1142/S0217751X07035008⟩. ⟨hal-03742312⟩
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