Note on Signature Change and Colombeau Theory

Recent work alludes to various `controversies' associated with signature change in general relativity. As we have argued previously, these are in fact disagreements about the (often unstated) assumptions underlying various possible approaches. The choice between approaches remains open.Comment: REVTex, 3 pages; to appear in GR

Reply Comment: Comparison of Approaches to Classical Signature Change

We contrast the two approaches to ``classical" signature change used by Hayward with the one used by us (Hellaby and Dray). There is (as yet) no rigorous derivation of appropriate distributional field equations. Hayward's distributional approach is based on a postulated modified form of the field equations. We make an alternative postulate. We point out an important difference between two possible philosophies of signature change --- ours is strictly classical, while Hayward's Lagrangian approach adopts what amounts to an imaginary proper ``time" on one side of the signature change, as is explicitly done in quantum cosmology. We also explain why we chose to use the Darmois-Israel type junction conditions, rather than the Lichnerowicz type junction conditions favoured by Hayward. We show that the difference in results is entirely explained by the difference in philosophy (imaginary versus real Euclidean ``time"), and not by the difference in approach to junction conditions (Lichnerowicz with specific coordinates versus Darmois with general coordinates).Comment: 10 pages, latex, no figures. Replying to - "Comment on `Failure of Standard Conservation Laws at a Classical Change of Signature'", S.A. Hayward, Phys. Rev. D52, 7331-7332 (1995) (gr-qc/9606045

The Magnetization of Cu_2(C_5H_{12}N_2)_2Cl_4 : A Heisenberg Spin Ladder System

We study the magnetization of a Heisenberg spin ladder using exact diagonalization techniques, finding three distinct magnetic phases. We consider the results in relation to the experimental behaviour of the new copper compound Cu_2(C_5H_{12}N_2)_2Cl_4 and deduce that the compound is well described by such a model with a ratio of `chain' to `rung' bond strengths (J/J^\prime) of the order of 0.2, consistent with results from the magnetic susceptibility. The effects of temperature, spin impurities and additional diagonal bonds are presented and we give evidence that these diagonal bonds are indeed of a ferromagnetic nature.Comment: Latex file (4 pages), related figures (encapsulated postscript) appende

Noether Currents of Charged Spherical Black Holes

We calculate the Noether currents and charges for Einstein-Maxwell theory using a version of the Wald approach. In spherical symmetry, the choice of time can be taken as the Kodama vector. For the static case, the resulting combined Einstein-Maxwell charge is just the mass of the black hole. Using either a classically defined entropy or the Iyer-Wald selection rules, the entropy is found to be just a quarter of the area of the trapping horizon. We propose identifying the combined Noether charge as an energy associated with the Kodama time. For the extremal black hole case, we discuss the problem of Wald's rescaling of the surface gravity to define the entropy.Comment: 4 page

Cosmic ray feedback in the FIRE simulations: constraining cosmic ray propagation with GeV gamma ray emission

We present the implementation and the first results of cosmic ray (CR) feedback in the Feedback In Realistic Environments (FIRE) simulations. We investigate CR feedback in non-cosmological simulations of dwarf, sub-$L\star$ starburst, and $L\star$ galaxies with different propagation models, including advection, isotropic and anisotropic diffusion, and streaming along field lines with different transport coefficients. We simulate CR diffusion and streaming simultaneously in galaxies with high resolution, using a two moment method. We forward-model and compare to observations of $\gamma$-ray emission from nearby and starburst galaxies. We reproduce the $\gamma$-ray observations of dwarf and $L\star$ galaxies with constant isotropic diffusion coefficient $\kappa \sim 3\times 10^{29}\,{\rm cm^{2}\,s^{-1}}$. Advection-only and streaming-only models produce order-of-magnitude too large $\gamma$-ray luminosities in dwarf and $L\star$ galaxies. We show that in models that match the $\gamma$-ray observations, most CRs escape low-gas-density galaxies (e.g.\ dwarfs) before significant collisional losses, while starburst galaxies are CR proton calorimeters. While adiabatic losses can be significant, they occur only after CRs escape galaxies, so they are only of secondary importance for $\gamma$-ray emissivities. Models where CRs are ``trapped'' in the star-forming disk have lower star formation efficiency, but these models are ruled out by $\gamma$-ray observations. For models with constant $\kappa$ that match the $\gamma$-ray observations, CRs form extended halos with scale heights of several kpc to several tens of kpc.Comment: 31 pages, 26 figures, accepted for publication in MNRA

An extreme critical space-time: echoing and black-hole perturbations

A homothetic, static, spherically symmetric solution to the massless Einstein- Klein-Gordon equations is described. There is a curvature singularity which is central, null, bifurcate and marginally trapped. The space-time is therefore extreme in the sense of lying at the threshold between black holes and naked singularities, just avoiding both. A linear perturbation analysis reveals two types of dominant mode. One breaks the continuous self-similarity by periodic terms reminiscent of discrete self-similarity, with echoing period within a few percent of the value observed numerically in near-critical gravitational collapse. The other dominant mode explicitly produces a black hole, white hole, eternally naked singularity or regular dispersal, the latter indicating that the background is critical. The black hole is not static but has constant area, the corresponding mass being linear in the perturbation amplitudes, explicitly determining a unit critical exponent. It is argued that a central null singularity may be a feature of critical gravitational collapse.Comment: 6 revtex pages, 6 eps figure

Submillimetre galaxies in a hierarchical universe: number counts, redshift distribution and implications for the IMF

High-redshift submillimetre galaxies (SMGs) are some of the most rapidly star-forming galaxies in the Universe. Historically, galaxy formation models have had difficulty explaining the observed number counts of SMGs. We combine a semi-empirical model with 3D hydrodynamical simulations and 3D dust radiative transfer to predict the number counts of unlensed SMGs. Because the stellar mass functions, gas and dust masses, and sizes of our galaxies are constrained to match observations, we can isolate uncertainties related to the dynamical evolution of galaxy mergers and the dust radiative transfer. The number counts and redshift distributions predicted by our model agree well with observations. Isolated disc galaxies dominate the faint (S_(1.1) ≲ 1 or S_(850) ≲ 2 mJy) population. The brighter sources are a mix of merger-induced starbursts and galaxy-pair SMGs; the latter subpopulation accounts for ∼30–50 per cent of all SMGs at all S_(1.1) ≳ 0.5 mJy (S_(850) ≳ 1 mJy). The mean redshifts are ∼3.0–3.5, depending on the flux cut, and the brightest sources tend to be at higher redshifts. Because the galaxy-pair SMGs will be resolved into multiple fainter sources by the Atacama Large Millimeter/submillimeter Array (ALMA), the bright ALMA counts should be as much as two times less than those observed using single-dish telescopes. The agreement between our model, which uses a Kroupa initial mass function (IMF), and observations suggests that the IMF in high-redshift starbursts need not be top heavy; if the IMF were top heavy, our model would overpredict the number counts. We conclude that the difficulty some models have reproducing the observed SMG counts is likely indicative of more general problems – such as an underprediction of the abundance of massive galaxies or a star formation rate and stellar mass relation normalization lower than that observed – rather than a problem specific to the SMG population

Comment on `Smooth and Discontinuous Signature Type Change in General Relativity'

Kossowski and Kriele derived boundary conditions on the metric at a surface of signature change. We point out that their derivation is based not only on certain smoothness assumptions but also on a postulated form of the Einstein field equations. Since there is no canonical form of the field equations at a change of signature, their conclusions are not inescapable. We show here that a weaker formulation is possible, in which less restrictive smoothness assumptions are made, and (a slightly different form of) the Einstein field equations are satisfied. In particular, in this formulation it is possible to have a bounded energy-momentum tensor at a change of signature without satisfying their condition that the extrinsic curvature vanish.Comment: Plain TeX, 6 pages; Comment on Kossowski and Kriele: Class. Quantum Grav. 10, 2363 (1993); Reply by Kriele: Gen. Rel. Grav. 28, 1409-1413 (1996