Black holes in vector-tensor theories and their thermodynamics

In this paper, we study Einstein gravity either minimally or non-minimally coupled to a vector field which breaks the gauge symmetry explicitly in general dimensions. We first consider a minimal theory which is simply the Einstein-Proca theory extended with a quartic self-interaction term for the vector field. We obtain its general static maximally symmetric black hole solution and study the thermodynamics using Wald formalism. The aspects of the solution are much like a Reissner-Nordstr{\o}m black hole in spite of that a global charge cannot be defined for the vector. For non-minimal theories, we obtain a lot of exact black hole solutions, depending on the parameters of the theories. In particular, many of the solutions are general static and have maximal symmetry. However, there are some subtleties and ambiguities in the derivation of the first laws because the existence of an algebraic degree of freedom of the vector in general invalids the Wald entropy formula. The thermodynamics of these solutions deserves further studies.Comment: to appera in EPJC, major revisions, referecens added. 33 page

Services Policy Reform in the People’s Republic of China: Before and After the Global Financial Crisis

Adverse effects of the global financial crisis on international trade include falling demand, increased trade protectionism, and drying up of trade finance. Much attention has focused on the impact of the crisis on goods trade; however literature on its impact on services trade is limited, especially on the services trade in the People’s Republic of China (PRC). This paper analyzes the impact of the global financial crisis on the PRC’s services trade, discusses the government’s policy responses, and raises policy suggestions.prc services policy; services trade; global financial crisis; international trade