Gauge dependence in the theory of non-linear spacetime perturbations

Diffeomorphism freedom induces a gauge dependence in the theory of spacetime perturbations. We derive a compact formula for gauge transformations of perturbations of arbitrary order. To this end, we develop the theory of Taylor expansions for one-parameter families (not necessarily groups) of diffeomorphisms. First, we introduce the notion of knight diffeomorphism, that generalises the usual concept of flow, and prove a Taylor's formula for the action of a knight on a general tensor field. Then, we show that any one-parameter family of diffeomorphisms can be approximated by a family of suitable knights. Since in perturbation theory the gauge freedom is given by a one-parameter family of diffeomorphisms, the expansion of knights is used to derive our transformation formula. The problem of gauge dependence is a purely kinematical one, therefore our treatment is valid not only in general relativity, but in any spacetime theory.Comment: paper accepted for publication in Communications of Mathematical Physics; SISSA preprint 105/97/A. 10 pages and 2 figures, standard late

Unexpectedly large surface gravities for acoustic horizons?

Acoustic black holes are fluid dynamic analogs of general relativistic black holes, wherein the behaviour of sound waves in a moving fluid acts as an analog for scalar fields propagating in a gravitational background. Acoustic horizons possess many of the properties more normally associated with the event horizons of general relativity, up to and including Hawking radiation. They have received much attention because it would seem to be much easier to experimentally create an acoustic horizon than to create an event horizon. We wish to point out some potential difficulties (and opportunities) in actually setting up an experiment that possesses an acoustic horizon. We show that in zero-viscosity, stationary fluid flow with generic boundary conditions, the creation of an acoustic horizon is accompanied by a formally infinite ``surface gravity'', and a formally infinite Hawking flux. Only by applying a suitable non-constant external body force, and for very specific boundary conditions on the flow, can these quantities be kept finite. This problem is ameliorated in more realistic models of the fluid. For instance, adding viscosity always makes the Hawking flux finite, but greatly complicates the behaviour of the acoustic radiation --- viscosity is tantamount to explicitly breaking ``acoustic Lorentz invariance''. Thus, this issue represents both a difficulty and an opportunity --- acoustic horizons may be somewhat more difficult to form than naively envisaged, but if formed, they may be much easier to detect than one would at first suppose.Comment: Plain LaTeX2e, 32 pages, 10 encapsulated postscript figures; Revised in view of referee comments; More discussion, (role of viscosity, relationship with other models), more references; physics and presentation clarified but central conclusions unaltere

Deriving relativistic momentum and energy. II. Three-dimensional case

We generalise a recent derivation of the relativistic expressions for momentum and kinetic energy from the one-dimensional to the three-dimensional case.Comment: 7 page

Optical geometry analysis of the electromagnetic self-force

We present an analysis of the behaviour of the electromagnetic self-force for charged particles in a conformally static spacetime, interpreting the results with the help of optical geometry. Some conditions for the vanishing of the local terms in the self-force are derived and discussed.Comment: 18 pages; 2 figure

Hawking-like radiation from evolving black holes and compact horizonless objects

Usually, Hawking radiation is derived assuming (i) that a future eternal event horizon forms, and (ii) that the subsequent exterior geometry is static. However, one may be interested in either considering quasi-black holes (objects in an ever-lasting state of approach to horizon formation, but never quite forming one), where (i) fails, or, following the evolution of a black hole during evaporation, where (ii) fails. We shall verify that as long as one has an approximately exponential relation between the affine parameters on the null generators of past and future null infinity, then subject to a suitable adiabatic condition being satisfied, a Planck-distributed flux of Hawking-like radiation will occur. This happens both for the case of an evaporating black hole, as well as for the more dramatic case of a collapsing object for which no horizon has yet formed (or even will ever form). In this article we shall cast the previous statement in a more precise and quantitative form, and subsequently provide several explicit calculations to show how the time-dependent Bogoliubov coefficients can be calculated.Comment: V1: 34 pages. V2: 35 pages; several additional references added; this version accepted for publication in JHE

On Relativistic Perturbations of Second and Higher Order

We present the results of a study of the gauge dependence of spacetime perturbations. In particular, we consider gauge invariance in general, we give a generating formula for gauge transformations to an arbitrary order n, and explicit transformation rules at second order.Comment: 6 pages, latex, with special style included, Proceedings of the 12th Italian Conference on General Relativity and Gravitational Physic

Total quantum state in the Einstein-Podolsky-Rosen-Bohm experiment with identical particles

The spin state in the Einstein-Podolsky-Rosen-Bohm gedankenexperiment with identical particles is supplemented by the spatial part. This allows one to extract all the information needed in a typical EPR argument, without requiring semi-intuitive steps. Local spin operators are introduced, to describe measurements of spin in given regions of space

A study of the effects of chronic neuroinflammation on cognition and behaviour in the GFAP-IL6 transgenic mouse and investigation of the flavonoid apigenin as a neuroprotective agent

Neuroinflammation is a prominent feature of most neurodegenerative and affective disorders and has been increasingly implicated as a contributing factor in the disease development. The inflammatory process is closely linked with multiple neurodegenerative pathways and represents an important therapeutic target in halting or reversing disease progression. This study explored the cognitive and behavioural effects of chronic neuroinflammation in the glial fibrillary acidic protein promoter-interleukin 6 (GFAP-IL6) transgenic mouse in which the pro-inflammatory cytokine interleukin 6 (IL-6) is overexpressed causing low level, chronic inflammation localised to the brain. Additionally the anti-inflammatory, anti-oxidant and neuroprotective potential of the dietary bioflavanoid apigenin was investigated to determine whether any deficits in behaviour and cognition could be rescued. Male and female heterozygous GFAP-IL6 mice (n=32) and their non-transgenic littermates (C57/BL6J) (n=36) were introduced to either an apigenin enriched pellet diet (40mg/kg daily dose) or control pellet diet at the age of 3 months. After 3 months of feeding (6 months of age) the mice were subjected to a behavioural test battery including the elevated plus maze (EPM), open field test (OF), Barnes maze (BM) and functional observational tests. The results showed that at 6 months of age, GFAP-IL6 mice exhibited alterations in anxiety-related behaviour in the EPM and OF, presenting a tendency toward an anxiolytic-like phenotype and demonstrated impairments in memory and spatial learning in the BM. GFAP-IL6 mice also displayed an ataxic phenotype and exhibited reduced locomotor activity compared to wild-type (WT) controls. The effect of apigenin on anxiety-related behaviours were mixed, being sedative-like in reducing locomotion and explorative behaviour in the EPM and OF, and anxiolytic-like in reducing risk assessment behaviour. Cognition improving properties are indicated for apigenin in the BM probe trial, enhancing recall of the target hole location, particularly among GFAP-IL6 mice. Interestingly, apigenin was additionally associated with increased food consumption and weight gain, suggesting potential as an appetite stimulant

Avaliação da solicitação de exames de sangue na UTI do HU-UFSC em pacientes com menos de 60 anos de idade.

Trabalho de Conclusão de Curso - Universidade Federal de Santa Catarina. Curso de Medicina. Departamento de Clínica Médica