Comments on gauge-invariance in cosmology

We revisit the gauge issue in cosmological perturbation theory, and highlight its relation to the notion of covariance in general relativity. We also discuss the similarities and differences of the covariant approach in perturbation theory to the Bardeen or metric approach in a non-technical fashion.Comment: 7 pages, 1 figure, revtex4; v3: minor changes, typos corrected, discussion extended; v4: typos corrected, corresponding to published versio

Piecewise Conserved Quantities

We review the treatment of conservation laws in spacetimes that are glued together in various ways, thus adding a boundary term to the usual conservation laws. Several examples of such spacetimes will be described, including the joining of Schwarzschild spacetimes of different masses, and the possibility of joining regions of different signatures. The opportunity will also be taken to explore some of the less obvious properties of Lorentzian vector calculus.Comment: To appear in Gravity and the Quantum, Springer 2017 (http://www.springer.com/in/book/9783319516998

Regular spherical dust spacetimes

Physical (and weak) regularity conditions are used to determine and classify all the possible types of spherically symmetric dust spacetimes in general relativity. This work unifies and completes various earlier results. The junction conditions are described for general non-comoving (and non-null) surfaces, and the limits of kinematical quantities are given on all comoving surfaces where there is Darmois matching. We show that an inhomogeneous generalisation of the Kantowski-Sachs metric may be joined to the Lemaitre-Tolman-Bondi metric. All the possible spacetimes are explicitly divided into four groups according to topology, including a group in which the spatial sections have the topology of a 3-torus. The recollapse conjecture (for these spacetimes) follows naturally in this approach.Comment: Minor improvements, additional references. Accepted by GR

The Algorithmic Origins of Life

Although it has been notoriously difficult to pin down precisely what it is that makes life so distinctive and remarkable, there is general agreement that its informational aspect is one key property, perhaps the key property. The unique informational narrative of living systems suggests that life may be characterized by context-dependent causal influences, and in particular, that top-down (or downward) causation -- where higher-levels influence and constrain the dynamics of lower-levels in organizational hierarchies -- may be a major contributor to the hierarchal structure of living systems. Here we propose that the origin of life may correspond to a physical transition associated with a shift in causal structure, where information gains direct, and context-dependent causal efficacy over the matter it is instantiated in. Such a transition may be akin to more traditional physical transitions (e.g. thermodynamic phase transitions), with the crucial distinction that determining which phase (non-life or life) a given system is in requires dynamical information and therefore can only be inferred by identifying causal architecture. We discuss some potential novel research directions based on this hypothesis, including potential measures of such a transition that may be amenable to laboratory study, and how the proposed mechanism corresponds to the onset of the unique mode of (algorithmic) information processing characteristic of living systems.Comment: 13 pages, 1 tabl

Optical Astronomy in Post-Apartheid South Africa: 1994 to 2004

The progress of optical astronomy in post-apartheid South Africa is discussed. Particular emphasis is given to the socio-political climate which embraced the idea of a 10-m class telescope as a flagship project that would lead to widespread development in science, technology and education - not only in South Africa, but across the subcontinent.Comment: 19 pages, 5 figures, to appear in: Organizations and Strategies in Astronomy, Vol. 5 (Ed.) A. Heck, Kluwer Acad. Pub

Characteristic Energy of the Coulomb Interactions and the Pileup of States

Tunneling data on $\mathrm{La_{1.28}Sr_{1.72}Mn_2O_7}$ crystals confirm Coulomb interaction effects through the $\sqrt{\mathrm{E}}$ dependence of the density of states. Importantly, the data and analysis at high energy, E, show a pileup of states: most of the states removed from near the Fermi level are found between ~40 and 130 meV, from which we infer the possibility of universal behavior. The agreement of our tunneling data with recent photoemission results further confirms our analysis.Comment: 4 pages, 4 figures, submitted to PR

Gravito-electromagnetic analogies

We reexamine and further develop different gravito-electromagnetic (GEM) analogies found in the literature, and clarify the connection between them. Special emphasis is placed in two exact physical analogies: the analogy based on inertial fields from the so-called "1+3 formalism", and the analogy based on tidal tensors. Both are reformulated, extended and generalized. We write in both formalisms the Maxwell and the full exact Einstein field equations with sources, plus the algebraic Bianchi identities, which are cast as the source-free equations for the gravitational field. New results within each approach are unveiled. The well known analogy between linearized gravity and electromagnetism in Lorentz frames is obtained as a limiting case of the exact ones. The formal analogies between the Maxwell and Weyl tensors are also discussed, and, together with insight from the other approaches, used to physically interpret gravitational radiation. The precise conditions under which a similarity between gravity and electromagnetism occurs are discussed, and we conclude by summarizing the main outcome of each approach.Comment: 60 pages, 2 figures. Improved version (compared to v2) with some re-write, notation improvements and a new figure that match the published version; expanded compared to the published version to include Secs. 2.3 and

The magnetic part of the Weyl tensor, and the expansion of discrete universes

42 pages, 27 figures42 pages, 27 figures42 pages, 27 figures42 pages, 27 figures42 pages, 27 figures42 pages, 27 figuresTC is supported by the STFC and DG by an AARMS postdoctoral fellowship

Relativistic cosmological perturbation scheme on a general background: scalar perturbations for irrotational dust

In standard perturbation approaches and N-body simulations, inhomogeneities are described to evolve on a predefined background cosmology, commonly taken as the homogeneous-isotropic solutions of Einstein's field equations (Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmologies). In order to make physical sense, this background cosmology must provide a reasonable description of the effective, i.e. spatially averaged, evolution of structure inhomogeneities also in the nonlinear regime. Guided by the insights that (i) the average over an inhomogeneous distribution of matter and geometry is in general not given by a homogeneous solution of general relativity, and that (ii) the class of FLRW cosmologies is not only locally but also globally gravitationally unstable in relevant cases, we here develop a perturbation approach that describes the evolution of inhomogeneities on a general background being defined by the spatially averaged evolution equations. This physical background interacts with the formation of structures. We derive and discuss the resulting perturbation scheme for the matter model `irrotational dust' in the Lagrangian picture, restricting our attention to scalar perturbations.Comment: 18 pages. Matches published version in CQ

Fluids in cosmology

We review the role of fluids in cosmology by first introducing them in General Relativity and then by applying them to a FRW Universe's model. We describe how relativistic and non-relativistic components evolve in the background dynamics. We also introduce scalar fields to show that they are able to yield an inflationary dynamics at very early times (inflation) and late times (quintessence). Then, we proceed to study the thermodynamical properties of the fluids and, lastly, its perturbed kinematics. We make emphasis in the constrictions of parameters by recent cosmological probes.Comment: 34 pages, 4 figures, version accepted as invited review to the book "Computational and Experimental Fluid Mechanics with Applications to Physics, Engineering and the Environment". Version 2: typos corrected and references expande