We present a tetrad-based method for solving the Einstein field equations for spherically-symmetric systems and compare it with the widely-used Lemaître-Tolman-Bondi (LTB) model. In particular, we focus on the issues of gauge ambiguity and the use of comoving versus 'physical' coordinate systems. We also clarify the correspondences between the two approaches, and illustrate their differences by applying them to the classic examples of the Schwarzschild and Friedmann-Lemaître-Robertson-Walker spacetimes. We demonstrate that the tetrad-based method does not suffer from the gauge freedoms inherent to the LTB model, naturally accommodates non-uniform pressure and has a more transparent physical interpretation. We further apply our tetrad-based method to a generalised form of 'Swiss cheese' model, which consists of an interior spherical region surrounded by a spherical shell of vacuum that is embedded in an exterior background universe. In general, we allow the fluid in the interior and exterior regions to support pressure, and do not demand that the interior region be compensated. We pay particular attention to the form of the solution in the intervening vacuum region and illustrate the validity of Birkhoff's theorem at both the metric and tetrad level. We then reconsider critically the original theoretical arguments underlying the so-called R h = ct cosmological model, which has recently B Do Young Kim

Fundamental to all living organisms and living soft matter are emergent processes in which the reorganization of individual constituents at the nanoscale drives group-level movements and shape changes at the macroscale over time. However, light-induced degradation of fluorophores, photobleaching, is a significant problem in extended bioimaging in life science. Here, we report opening a long-time investigation window by nonbleaching phase intensity nanoscope: PINE. We accomplish phase-intensity separation such that nanoprobe distributions are distinguished by an integrated phase-intensity multilayer thin film (polyvinyl alcohol/liquid crystal). We overcame a physical limit to resolve sub-10 nm cellular architectures, and achieve the first dynamic imaging of nanoscopic reorganization over 250 h using PINE. We discover nanoscopic rearrangements synchronized with the emergence of group-level movements and shape changes at the macroscale according to a set of interaction rules with importance in cellular and soft matter reorganization, self-organization, and pattern formation.