Exponential Metric Fields

The Laser Interferometer Space Antenna (LISA) mission will use advanced technologies to achieve its science goals: the direct detection of gravitational waves, the observation of signals from compact (small and dense) stars as they spiral into black holes, the study of the role of massive black holes in galaxy evolution, the search for gravitational wave emission from the early Universe. The gravitational red-shift, the advance of the perihelion of Mercury, deflection of light and the time delay of radar signals are the classical tests in the first order of General Relativity (GR). However, LISA can possibly test Einstein's theories in the second order and perhaps, it will show some particular feature of non-linearity of gravitational interaction. In the present work we are seeking a method to construct theoretical templates that limit in the first order the tensorial structure of some metric fields, thus the non-linear terms are given by exponential functions of gravitational strength. The Newtonian limit obtained here, in the first order, is equivalent to GR.Comment: Accepted for publication in Astrophysics and Space Science, 17 page

Shopping externalities and retail concentration:Evidence from dutch shopping streets

Why do shops cluster in shopping streets? We argue that retail firms benefit from shopping externalities. We identify these externalities for the main Dutch shopping streets by estimating the effect of footfall – the number of pedestrians that pass by – and the number of shops in the vicinity on store owners’ rental income. We address endogeneity issues by exploiting spatial variation within shopping streets combined with historic long-lagged instruments. Our estimates imply an elasticity of rental income with respect to footfall as well as number of shops in the vicinity of (at least) 0.25. We show that these shopping externalities are unlikely to be internalised. It follows that substantial subsidies to shop owners are welfare improving, seemingly justifying current policies. Finally, we find limited evidence for heterogeneity between retail firms located in shopping streets in their willingness to pay for shopping externalities