First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations

We prescribe a choice of 18 variables in all that casts the equations of the fully nonlinear characteristic formulation of general relativity in first--order quasi-linear canonical form. At the analytical level, a formulation of this type allows us to make concrete statements about existence of solutions. In addition, it offers concrete advantages for numerical applications as it now becomes possible to incorporate advanced numerical techniques for first order systems, which had thus far not been applicable to the characteristic problem of the Einstein equations, as well as in providing a framework for a unified treatment of the vacuum and matter problems. This is of relevance to the accurate simulation of gravitational waves emitted in astrophysical scenarios such as stellar core collapse.Comment: revtex4, 7 pages, text and references added, typos corrected, to appear in Phys. Rev.

Worldline approach to vector and antisymmetric tensor fields

The N=2 spinning particle action describes the propagation of antisymmetric tensor fields, including vector fields as a special case. In this paper we study the path integral quantization on a one-dimensional torus of the N=2 spinning particle coupled to spacetime gravity. The action has a local N=2 worldline supersymmetry with a gauged U(1) symmetry that includes a Chern-Simons coupling. Its quantization on the torus produces the one-loop effective action for a single antisymmetric tensor. We use this worldline representation to calculate the first few Seeley-DeWitt coefficients for antisymmetric tensor fields of arbitrary rank in arbitrary dimensions. As side results we obtain the correct trace anomaly of a spin 1 particle in four dimensions as well as exact duality relations between differential form gauge fields. This approach yields a drastic simplification over standard heat-kernel methods. It contains on top of the usual proper time a new modular parameter implementing the reduction to a single tensor field. Worldline methods are generically simpler and more efficient in perturbative computations then standard QFT Feynman rules. This is particularly evident when the coupling to gravity is considered.Comment: 30 pages, 5 figures, references adde

Higher spin fields from a worldline perspective

Higher spin fields in four dimensions, and more generally conformal fields in arbitrary dimensions, can be described by spinning particle models with a gauged SO(N) extended supergravity on the worldline. We consider here the one-loop quantization of these models by studying the corresponding partition function on the one-dimensional torus. After gauge fixing the supergravity multiplet, the partition function reduces to an integral over the corresponding moduli space which is computed using orthogonal polynomial techniques. We obtain a compact formula which gives the number of physical degrees of freedom for all N in all dimensions. As an aside we compute the physical degrees of freedom of the SO(4) = SU(2)xSU(2) model with only a SU(2) factor gauged, which has attracted some interest in the literature.Comment: 21 page

Magnetohydrodynamics and Plasma Cosmology

We study the linear magnetohydrodynamic (MHD) equations, both in the Newtonian and the general-relativistic limit, as regards a viscous magnetized fluid of finite conductivity and discuss instability criteria. In addition, we explore the excitation of cosmological perturbations in anisotropic spacetimes, in the presence of an ambient magnetic field. Acoustic, electromagnetic (e/m) and fast-magnetosonic modes, propagating normal to the magnetic field, can be excited, resulting in several implications of cosmological significance.Comment: 9 pages, RevTeX, To appear in the Proceedings of the Peyresq X Meeting, IJTP Conference Serie

Nonlinear coupled Alfv\'{e}n and gravitational waves

In this paper we consider nonlinear interaction between gravitational and electromagnetic waves in a strongly magnetized plasma. More specifically, we investigate the propagation of gravitational waves with the direction of propagation perpendicular to a background magnetic field, and the coupling to compressional Alfv\'{e}n waves. The gravitational waves are considered in the high frequency limit and the plasma is modelled by a multifluid description. We make a self-consistent, weakly nonlinear analysis of the Einstein-Maxwell system and derive a wave equation for the coupled gravitational and electromagnetic wave modes. A WKB-approximation is then applied and as a result we obtain the nonlinear Schr\"{o}dinger equation for the slowly varying wave amplitudes. The analysis is extended to 3D wave pulses, and we discuss the applications to radiation generated from pulsar binary mergers. It turns out that the electromagnetic radiation from a binary merger should experience a focusing effect, that in principle could be detected.Comment: 20 pages, revtex4, accepted in PR

Resonant interaction between gravitational waves, electromagnetic waves and plasma flows

In magnetized plasmas gravitational and electromagnetic waves may interact coherently and exchange energy between themselves and with plasma flows. We derive the wave interaction equations for these processes in the case of waves propagating perpendicular or parallel to the plasma background magnetic field. In the latter case, the electromagnetic waves are taken to be circularly polarized waves of arbitrary amplitude. We allow for a background drift flow of the plasma components which increases the number of possible evolution scenarios. The interaction equations are solved analytically and the characteristic time scales for conversion between gravitational and electromagnetic waves are found. In particular, it is shown that in the presence of a drift flow there are explosive instabilities resulting in the generation of gravitational and electromagnetic waves. Conversely, we show that energetic waves can interact to accelerate particles and thereby \emph{produce} a drift flow. The relevance of these results for astrophysical and cosmological plasmas is discussed.Comment: 12 pages, 1 figure, typos corrected and numerical example adde

Integrated computer-aided working-fluid design and thermoeconomic ORC system optimisation

The successful commercialisation of organic Rankine cycle (ORC) systems across a range of power outputs and heat-source temperatures demands step-changes in both improved thermodynamic performance and reduced investment costs. The former can be achieved through high-performance components and optimised system architectures operating with novel working-fluids, whilst the latter requires careful component-technology selection, economies of scale, learning curves and a proper selection of materials and cycle configurations. In this context, thermoeconomic optimisation of the whole power-system should be completed aimed at maximising profitability. This paper couples the computer-aided molecular design (CAMD) of the working-fluid with ORC thermodynamic models, including recuperated and other alternative (e.g., partial evaporation or trilateral) cycles, and a thermoeconomic system assessment. The developed CAMD-ORC framework integrates an advanced molecular-based group-contribution equation of state, SAFT-γ Mie, with a thermodynamic description of the system, and is capable of simultaneously optimising the working-fluid structure, and the thermodynamic system. The advantage of the proposed CAMD-ORC methodology is that it removes subjective and pre-emptive screening criteria that would otherwise exist in conventional working-fluid selection studies. The framework is used to optimise hydrocarbon working-fluids for three different heat sources (150, 250 and 350 °C, each with mcp = 4.2 kW/K). In each case, the optimal combination of working-fluid and ORC system architecture is identified, and system investment costs are evaluated through component sizing models. It is observed that optimal working fluids that minimise the specific investment cost (SIC) are not the same as those that maximise power output. For the three heat sources the optimal working-fluids that minimise the SIC are isobutane, 2-pentene and 2-heptene, with SICs of 4.03, 2.22 and 1.84 £/W respectively

VLA imaging of 12CO J = 1-0 and free-free emission in lensed submillimetre galaxies

We present a study using the Karl G. Jansky Very Large Array (VLA) of 12CO J = 1-0 emission in three strongly lensed submillimetre-selected galaxies (SMM J16359, SMM J14009 and SMM J02399) at z = 2.5-2.9. These galaxies span LIR = 1011-1013 L⊙, offering an opportunity to compare the interstellar medium of luminous infrared galaxies and ultraluminous infrared galaxies at high redshift. We estimate molecular gas masses in the range of 2-40 × 109 M⊙ using a method that assumes canonical underlying brightness temperature (Tb) ratios for star-forming and non-star-forming gas phases and a maximal star formation efficiency. A more simplistic method - using XCO = 0.8 and the measured Tb ratios - yields gas masses twice as high. In SMM J14009 we find L CO 3-2'/L CO 1-0'=0.95±0.12, indicative of warm, star-forming gas, possibly influenced by the central active galactic nucleus (AGN). We set a gas mass limit of 3σ < 6 × 108 M⊙ for the Lyman break galaxy, A2218 #384, located in the same field as SMM J16359 at z = 2.515. Finally, we use the rest-frame ˜115 GHz free-free flux densities for SMM J14009 and SMM J02399 - measurements tied directly to the photoionization rate of massive stars, and made possible by VLA's bandwidth - to estimate star formation rates (SFRs) of 400-600 M⊙ yr-1 and to estimate the fraction of LIR due to AGN

The fuzzy S^2 structure of M2-M5 systems in ABJM membrane theories

We analyse the fluctuations of the ground-state/funnel solutions proposed to describe M2-M5 systems in the level-k mass-deformed/pure Chern-Simons-matter ABJM theory of multiple membranes. We show that in the large N limit the fluctuations approach the space of functions on the 2-sphere rather than the naively expected 3-sphere. This is a novel realisation of the fuzzy 2-sphere in the context of Matrix Theories, which uses bifundamental instead of adjoint scalars. Starting from the multiple M2-brane action, a U(1) Yang-Mills theory on R^{2,1} x S^2 is recovered at large N, which is consistent with a single D4-brane interpretation in Type IIA string theory. This is as expected at large k, where the semiclassical analysis is valid. Several aspects of the fluctuation analysis, the ground-state/funnel solutions and the mass-deformed/pure ABJM equations can be understood in terms of a discrete noncommutative realisation of the Hopf fibration. We discuss the implications for the possibility of finding an M2-brane worldvolume derivation of the classical S^3 geometry of the M2-M5 system. Using a rewriting of the equations of the SO(4)-covariant fuzzy 3-sphere construction, we also directly compare this fuzzy 3-sphere against the ABJM ground-state/funnel solutions and show them to be different.Comment: 60 pages, Latex; v2: references added; v3: typos corrected and references adde

Relativistic Hydrodynamic Evolutions with Black Hole Excision

We present a numerical code designed to study astrophysical phenomena involving dynamical spacetimes containing black holes in the presence of relativistic hydrodynamic matter. We present evolutions of the collapse of a fluid star from the onset of collapse to the settling of the resulting black hole to a final stationary state. In order to evolve stably after the black hole forms, we excise a region inside the hole before a singularity is encountered. This excision region is introduced after the appearance of an apparent horizon, but while a significant amount of matter remains outside the hole. We test our code by evolving accurately a vacuum Schwarzschild black hole, a relativistic Bondi accretion flow onto a black hole, Oppenheimer-Snyder dust collapse, and the collapse of nonrotating and rotating stars. These systems are tracked reliably for hundreds of M following excision, where M is the mass of the black hole. We perform these tests both in axisymmetry and in full 3+1 dimensions. We then apply our code to study the effect of the stellar spin parameter J/M^2 on the final outcome of gravitational collapse of rapidly rotating n = 1 polytropes. We find that a black hole forms only if J/M^2<1, in agreement with previous simulations. When J/M^2>1, the collapsing star forms a torus which fragments into nonaxisymmetric clumps, capable of generating appreciable ``splash'' gravitational radiation.Comment: 17 pages, 14 figures, submitted to PR