Weyl gravity has been advanced in the recent past as an alternative to General Relativity (GR). The theory has had some success in fitting galactic rotation curves without the need for copious amounts of dark matter. To check the viability of Weyl gravity, we propose two additional classical tests of the theory: the deflection of light and time delay in the exterior of a static spherically symmetric source. The result for the deflection of light is remarkably simple: besides the usual positive (attractive) Einstein deflection of 4GM/r 0 we obtain an extra deflection term of −γr 0 where γ is a constant and r 0 is the radius of closest approach. With a negative γ, the extra term can increase the deflection on large distance scales (galactic or greater) and therefore imitate the effect of dark matter. Notably, the negative sign required for γ is opposite to the sign of γ used to fit galactic rotation curves. The experimental constraints show explicitly that the magnitude of γ is of the order of the inverse Hubble length something already noted as an interesting numerical coincidence in the fitting of galactic rotation curves [9].
We study the Casimir piston for massless scalar fields obeying Dirichlet
boundary conditions in a three dimensional cavity with sides of arbitrary
lengths $a,b$ and $c$ where $a$ is the plate separation. We obtain an exact
expression for the Casimir force on the piston valid for any values of the
three lengths. As in the electromagnetic case with perfect conductor
conditions, we find that the Casimir force is negative (attractive) regardless
of the values of $a$, $b$ and $c$. Though cases exist where the interior
contributes a positive (repulsive) Casimir force, the total Casimir force on
the piston is negative when the exterior contribution is included. We also
obtain an alternative expression for the Casimir force that is useful
computationally when the plate separation $a$ is large.Comment: 19 pages,3 figures; references updated and typos fixed to match
published versio
Perfect magnetic conductor (PMC) boundary conditions are dual to the more familiar perfect electric conductor (PEC) conditions and can be viewed as the electromagnetic analog of the boundary conditions in the bag model for hadrons in QCD. Recent advances and requirements in communication technologies have attracted great interest in PMC's and Casimir experiments involving structures that approximate PMC's may be carried out in the not too distant future. In this paper, we make a study of the zero-temperature PMC Casimir piston in d + 1 dimensions. The PMC Casimir energy is explicitly evaluated by summing over p + 1-dimensional Dirichlet energies where p ranges from 2 to d inclusively. We derive two exact d-dimensional expressions for the Casimir force on the piston and find that the force is negative (attractive) in all dimensions. Both expressions are applied to the case of 2+1 and 3+1 dimensions. A spin-off from our work is a contribution to the PEC literature: we obtain a useful alternative expression for the PEC Casimir piston in 3+1 dimensions and also evaluate the Casimir force per unit area on an infinite strip, a geometry of experimental interest. *
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.