Stochastically Fluctuating Black-Hole Geometry, Hawking Radiation and the Trans-Planckian Problem

We study the propagation of null rays and massless fields in a black hole fluctuating geometry. The metric fluctuations are induced by a small oscillating incoming flux of energy. The flux also induces black hole mass oscillations around its average value. We assume that the metric fluctuations are described by a statistical ensemble. The stochastic variables are the phases and the amplitudes of Fourier modes of the fluctuations. By averaging over these variables, we obtain an effective propagation for massless fields which is characterized by a critical length defined by the amplitude of the metric fluctuations: Smooth wave packets with respect to this length are not significantly affected when they are propagated forward in time. Concomitantly, we find that the asymptotic properties of Hawking radiation are not severely modified. However, backward propagated wave packets are dissipated by the metric fluctuations once their blue shifted frequency reaches the inverse critical length. All these properties bear many resemblences with those obtained in models for black hole radiation based on a modified dispersion relation. This strongly suggests that the physical origin of these models, which were introduced to confront the trans-Planckian problem, comes from the fluctuations of the black hole geometry.Comment: 32 page

The Prevalence and Molecular Spectrum of α- and β-Globin Gene Mutations in 14,332 Families of Guangdong Province, China

OBJECTIVE: To reveal the familial prevalence and molecular variation of α- and β-globin gene mutations in Guangdong Province. METHODS: A total of 40,808 blood samples from 14,332 families were obtained and analyzed for both hematological and molecular parameters. RESULTS: A high prevalence of α- and β-globin gene mutations was found. Overall, 17.70% of pregnant women, 15.94% of their husbands, 16.03% of neonates, and 16.83% of couples (pregnant women and their husbands) were heterozygous carriers of α- or β-thalassemia. The regions with the highest prevalence were the mountainous and western regions, followed by the Pearl River Delta; the region with the lowest prevalence was Chaoshan. The total familial carrier rate (both spouses were α- or β-thalassemia carriers) was 1.87%, and the individual carrier rates of α- and β-thalassemia were 1.68% and 0.20%, respectively. The total rate of moderate-to-severe fetal thalassemia was 12.78% among couples in which both parents were carriers. CONCLUSIONS: There was a high prevalence of α- and β-thalassemia in Guangdong Province. This study will contribute to the development of thalassemia prevention and control strategies in Guangdong Province