Black Hole Radiation with Modified Dispersion Relation in Tunneling Paradigm: Free-fall Frame

Due to the exponential high gravitational red shift near the event horizon of a black hole, it might appear that the Hawking radiation would be highly sensitive to some unknown high energy physics. To study effects of any unknown physics at the Planck scale on the Hawking radiation, the dispersive field theory models have been proposed, which are variations of Unruh's sonic black hole analogy. In this paper, we use the Hamilton-Jacobi method to investigate the dispersive field theory models. The preferred frame is the free-fall frame of the black hole. The dispersion relation adopted agrees with the relativistic one at low energy but is modified near the Planck mass $m_{p}$. The corrections to the Hawking temperature are calculated for massive and charged particles to $\mathcal{O}\left( m_{p}^{-2}\right)$ and neutral and massless particles with $\lambda=0$ to all orders. The Hawking temperature of radiation agrees with the standard one at the leading order. After the spectrum of radiation near the horizon is obtained, we use the brick wall model to compute the thermal entropy of a massless scalar field near the horizon of a 4D spherically symmetric black hole and a 2D one. Finally, the luminosity of a Schwarzschild black hole is calculated by using the geometric optics approximation.Comment: 28 pages. arXiv admin note: substantial text overlap with arXiv:1505.0304

The impacts of carbon emissions on global manufacturing value chain relocation: Theoretical and empirical development of a meso-level model

As a stark contrast to the diminishing media profile of the UN climate change talks, the global manufacturers appear to have become more carbon aware than ever before. Carbon audits have been carried out within many corporations to assess the carbon intensity of production processes. This is partly to address cost issues of the present (i.e. the recent rise in fossil fuel prices) and of the future (e.g. new carbon related taxes and trade tariffs). Moreover, the adoption of low carbon, clean manufacturing processes has become an increasingly prominent part of branding for many products, which could affect market share and business performance in ways that go beyond questions of cost competitiveness. How will this carbon awareness affect the configuration of the value chains of global manufacturing? Will the individual manufacturers’ decisions lead to an effective reduction of total carbon emissions at the global value chain scale? Our paper aims to answer these questions through developing a theoretical model and testing it empirically through case studies of global value chains. The model accounts explicitly costs of energy, carbon, other intermediate inputs and primary inputs in the production and transport of each component, product assembly and delivery to the market. Much work has been done on the value chain location problem – e.g. on the production unbundling among different countries from a macro-economic perspective, or on operations management at the microscopic or individual manufacturer level. It is only until recently that the economic and technology aspects have been combined in the study of global value chains (for example in the paper by Baldwin and Venables in last year’s ERSA Congress). The appropriate spatial scale for our research questions would appear to be at a meso-level: i.e. the model goes beyond the micro-level operational analysis of a single plant to cover the entire value chain for a given product, but does not cover the full interactions at the macro level. This perspective is relatively rare in the literature and provides a tool that connects the micro level and macro level perspectives.