Quantum effects of black holes and the cosmological constant problem

A quantum equation of gravity is proposed using geometric quantization of general relativity. Quantum equation for a black hole is solved using the Wentzel-Kramers-Brillouin (WKB) method. Quantum effects of a Schwarzschild black hole are provided by solving a quantum equation of gravity requiring a stationary phase and also using the Einstein-Brillouin-Keller (EBK) quantization condition, and they are consistent each other. WKB method is also applied to the McVittie-Thakurta metric, which is describing a system consists of Schwarzschild black holes and a scalar field. A possible interplay between quantum black holes and scalar field are investigated in detail. A number density of black holes in the universe is obtained using statistical mechanics on a system consisting of black holes and a scalar filed. A possible solution for the cosmological constant problem is proposed in basis of a statistical consideration.Comment: 13 pages, 1 figur

Fragmentation in a product cycle model

We develop a simple model in which fragmentation, innovation and imitation take in place simultaneously. Firms in North fragment their business into two parts: assembly and services. A reduction in the cost of services to coordinate fragmented businesses between North and South does not enhance fragmentation. On the contrary, the arrival rate of imitation accelerates and that of innovation slows down. Consequently, the life of Northern goods becomes shorter and that of Southern copies becomes longer. We also derive other results to compare to those in Grossman and Helpman (1991) and in Glass and Saggi (2001).Coordinatin Costs