Long term stable integration of a maximally sliced Schwarzschild black hole using a smooth lattice method

We will present results of a numerical integration of a maximally sliced Schwarzschild black hole using a smooth lattice method. The results show no signs of any instability forming during the evolutions to t=1000m. The principle features of our method are i) the use of a lattice to record the geometry, ii) the use of local Riemann normal coordinates to apply the 1+1 ADM equations to the lattice and iii) the use of the Bianchi identities to assist in the computation of the curvatures. No other special techniques are used. The evolution is unconstrained and the ADM equations are used in their standard form.Comment: 47 pages including 26 figures, plain TeX, also available at http://www.maths.monash.edu.au/~leo/preprint

The Hamiltonian formulation of General Relativity: myths and reality

A conventional wisdom often perpetuated in the literature states that: (i) a 3+1 decomposition of space-time into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation of General Relativity (GR); (ii) the canonical treatment unavoidably breaks the symmetry between space and time in GR and the resulting algebra of constraints is not the algebra of four-dimensional diffeomorphism; (iii) according to some authors this algebra allows one to derive only spatial diffeomorphism or, according to others, a specific field-dependent and non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac [Proc. Roy. Soc. A 246 (1958) 333] and of ADM [Arnowitt, Deser and Misner, in "Gravitation: An Introduction to Current Research" (1962) 227] of the canonical structure of GR are equivalent. We provide some general reasons why these statements should be questioned. Points (i-iii) have been shown to be incorrect in [Kiriushcheva et al., Phys. Lett. A 372 (2008) 5101] and now we thoroughly re-examine all steps of the Dirac Hamiltonian formulation of GR. We show that points (i-iii) above cannot be attributed to the Dirac Hamiltonian formulation of GR. We also demonstrate that ADM and Dirac formulations are related by a transformation of phase-space variables from the metric $g_{\mu\nu}$ to lapse and shift functions and the three-metric $g_{km}$, which is not canonical. This proves that point (iv) is incorrect. Points (i-iii) are mere consequences of using a non-canonical change of variables and are not an intrinsic property of either the Hamilton-Dirac approach to constrained systems or Einstein's theory itself.Comment: References are added and updated, Introduction is extended, Subsection 3.5 is added, 83 pages; corresponds to the published versio

Evaluating Alternative Nutrient Sources in Subsistence-Level Aquaponic Systems

Many food production methods are both economically and environmentally unsustainable. Our project investigated aquaponics, an alternative method of agriculture that could address these issues. Aquaponics combines fish and plant crop production in a symbiotic, closed-loop system. We aimed to reduce the initial and operating costs of current aquaponic systems by utilizing alternative feeds. These improvements may allow for sustainable implementation of the system in rural or developing regions. We conducted a multi-phase process to determine the most affordable and effective feed alternatives for use in an aquaponic system. At the end of two preliminary phases, soybean meal was identified as the most effective potential feed supplement. In our final phase, we constructed and tested six full-scale aquaponic systems of our own design. Data showed that soybean meal can be used to reduce operating costs and reliance on fishmeal. However, a more targeted investigation is needed to identify the optimal formulation of alternative feed blends

Numerical Relativity: A review

Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of strong field scenarios and been crucial to reveal unexpected phenomena. Considerable efforts are being spent to simulate astrophysically relevant simulations, understand different aspects of the theory and even provide insights in the search for a quantum theory of gravity. In the present article I review the present status of the field of Numerical Relativity, describe the techniques most commonly used and discuss open problems and (some) future prospects.Comment: 2 References added; 1 corrected. 67 pages. To appear in Classical and Quantum Gravity. (uses iopart.cls

Limits on Einstein's equivalence principle from the first localized fast radio burst FRB 150418

Fast radio bursts (FRBs) have recently been used to place limits on Einstein’s Equivalence Principle via observations of time delays between photons of different radio frequencies by Wei et al. These limits on differential post-Newtonian parameters (Δγ < - 2.52 x 10 -8) are the best yet achieved, but they still rely on uncertain assumptions, namely the relative contributions of dispersion and gravitational delays to the observed time delays and the distances to FRBs. Also, very recently, the first FRB host galaxy has likely been identified, providing the first redshift-based distance estimate to FRB 150418. Moreover, consistency between the ΩIGM estimate from FRB 150418 and ΩIGM, expected from ΛCDM models and WMAP observations, leads one to conclude that the observed time delay for FRB 150418 is highly dominated by dispersion, with any gravitational delays being small contributors. This points to even tighter limits on Δγ. In this paper, the technique of Wei et al. is applied to FRB 150418 to produce a limit of Δγ < 1–2 × 10−9, approximately an order of magnitude better than previous limits and in line with expectations by Wei et al. for what could be achieved if the dispersive delay is separated from other effects. Future substantial improvements in such limits will depend on accurately determining the contribution of individual ionized components to the total observed time delays for FRBs

Dynamics of spherically symmetric spacetimes: hydrodynamics and radiation

Using the 3+1 formalism of general relativity we obtain the equations governing the dynamics of spherically symmetric spacetimes with arbitrary sources. We then specialize for the case of perfect fluids accompanied by a flow of interacting massless or massive particles (e.g. neutrinos) which are described in terms of relativistic transport theory. We focus in three types of coordinates: 1) isotropic gauge and maximal slicing, 2) radial gauge and polar slicing, and 3) isotropic gauge and polar slicing.Comment: submitted to Phys. Rev. D, 46 pages, RevTex file, no figure

Chronic, intermittent treatment with a cannabinoid receptor agonist impairs recognition memory and brain network functional connectivity

Elucidating how cannabinoids affect brain function is instrumental for the development of therapeutic tools aiming to mitigate 'on target' side effects of cannabinoid based therapies. A single treatment with the cannabinoid receptor agonist, WIN 55,212-2, disrupts recognition memory in mice. Here we evaluate how prolonged, intermittent (30 days) exposure to WIN 55,212-2 (1mg/kg) alters recognition memory and impacts on brain metabolism and functional connectivity. We show that chronic, intermittent treatment with WIN 55,212-2 disrupts recognition memory (Novel Object Recognition Test) without affecting locomotion and anxiety-like behaviour (Open Field and Elevated Plus Maze). Through 14 C-2-deoxyglucose functional brain imaging we show that chronic, intermittent WIN 55,212-2 exposure induces hypometabolism in the hippocampal dorsal subiculum and in the mediodorsal nucleus of the thalamus, two brain regions directly involved in recognition memory. In addition, WIN 55,212-2 exposure induces hypometabolism in the habenula with a contrasting hypermetabolism in the globus pallidus. Through the application of the Partial Least Squares Regression (PLSR) algorithm to the brain imaging data, we observed that prolonged WIN 55,212-2 administration alters functional connectivity in brain networks that underlie recognition memory, including that between the hippocampus and prefrontal cortex, the thalamus and prefrontal cortex, and between the hippocampus and the perirhinal cortex. In addition, our results support disturbed lateral habenula and serotonin system functional connectivity following WIN 55,212-2 exposure. Overall, this study provides new insight into the functional mechanisms underlying the impact of chronic cannabinoid exposure on memory and highlights the serotonin system as a particularly vulnerable target. This article is protected by copyright. All rights reserved

Galaxy bulges and their massive black holes: a review

With references to both key and oft-forgotten pioneering works, this article starts by presenting a review into how we came to believe in the existence of massive black holes at the centres of galaxies. It then presents the historical development of the near-linear (black hole)-(host spheroid) mass relation, before explaining why this has recently been dramatically revised. Past disagreement over the slope of the (black hole)-(velocity dispersion) relation is also explained, and the discovery of sub-structure within the (black hole)-(velocity dispersion) diagram is discussed. As the search for the fundamental connection between massive black holes and their host galaxies continues, the competing array of additional black hole mass scaling relations for samples of predominantly inactive galaxies are presented.Comment: Invited (15 Feb. 2014) review article (submitted 16 Nov. 2014). 590 references, 9 figures, 25 pages in emulateApJ format. To appear in "Galactic Bulges", E. Laurikainen, R.F. Peletier, and D.A. Gadotti (eds.), Springer Publishin

Comments on Theoretical Problems in Nonsymmetric Gravitational Theory

Damour, Deser and McCarthy have claimed that the nonsymmetric gravitational theory (NGT) is untenable due to curvature coupled ghost modes and bad asymptotic behavior. This claim is false for it is based on a physically inaccurate treatment of wave propagation on a curved background and an incorrect method for extracting asymptotic behavior. We show that the flux of gravitational radiation in NGT is finite in magnitude and positive in sign.Comment: 11 page