1+1+2 Electromagnetic perturbations on general LRS space-times: Regge-Wheeler and Bardeen-Press equations

We use the, covariant and gauge-invariant, 1+1+2 formalism developed by Clarkson and Barrett, and develop new techniques, to decouple electromagnetic (EM) perturbations on arbitrary locally rotationally symmetric (LRS) space-times. Ultimately, we derive 3 decoupled complex equations governing 3 complex scalars. One of these is a new Regge-Wheeler (RW) equation generalized for LRS space-times, whereas the remaining two are new generalizations of the Bardeen-Press (BP) equations. This is achieved by first using linear algebra techniques to rewrite the first-order Maxwell equations in a new complex 1+1+2 form which is conducive to decoupling. This new complex system immediately yields the generalized RW equation, and furthermore, we also derive a decoupled equation governing a newly defined complex EM 2-vector. Subsequently, a further decomposition of the 1+1+2 formalism into a 1+1+1+1 formalism is developed, allowing us to decompose the complex EM 2-vector, and its governing equations, into spin-weighted scalars, giving rise to the generalized BP equations

A Novel, Low-Volume Method for Organ Culture of Embryonic Kidneys That Allows Development of Cortico-Medullary Anatomical Organization

Here, we present a novel method for culturing kidneys in low volumes of medium that offers more organotypic development compared to conventional methods. Organ culture is a powerful technique for studying renal development. It recapitulates many aspects of early development very well, but the established techniques have some disadvantages: in particular, they require relatively large volumes (1–3 mls) of culture medium, which can make high-throughput screens expensive, they require porous (filter) substrates which are difficult to modify chemically, and the organs produced do not achieve good cortico-medullary zonation. Here, we present a technique of growing kidney rudiments in very low volumes of medium–around 85 microliters–using silicone chambers. In this system, kidneys grow directly on glass, grow larger than in conventional culture and develop a clear anatomical cortico-medullary zonation with extended loops of Henle