Weyssenhoff fluid dynamics in general relativity using a 1+3 covariant approach

The Weyssenhoff fluid is a perfect fluid with spin where the spin of the matter fields is the source of torsion in an Einstein-Cartan framework. Obukhov and Korotky showed that this fluid can be described as an effective fluid with spin in general relativity. A dynamical analysis of such a fluid is performed in a gauge invariant manner using the 1+3 covariant approach. This yields the propagation and constraint equations for the set of dynamical variables. A verification of these equations is performed for the special case of irrotational flow with zero peculiar acceleration by evolving the constraints.Comment: 20 page

Jupiter as an exoplanet: UV to NIR transmission spectrum reveals hazes, a Na layer and possibly stratospheric H2O-ice clouds

Currently, the analysis of transmission spectra is the most successful technique to probe the chemical composition of exoplanet atmospheres. But the accuracy of these measurements is constrained by observational limitations and the diversity of possible atmospheric compositions. Here we show the UV-VIS-IR transmission spectrum of Jupiter, as if it were a transiting exoplanet, obtained by observing one of its satellites, Ganymede, while passing through Jupiter's shadow i.e., during a solar eclipse from Ganymede. The spectrum shows strong extinction due to the presence of clouds (aerosols) and haze in the atmosphere, and strong absorption features from CH4. More interestingly, the comparison with radiative transfer models reveals a spectral signature, which we attribute here to a Jupiter stratospheric layer of crystalline H2O ice. The atomic transitions of Na are also present. These results are relevant for the modeling and interpretation of giant transiting exoplanets. They also open a new technique to explore the atmospheric composition of the upper layers of Jupiter's atmosphere.Comment: Accepted for publication in ApJ Letter

Analysis of unbounded operators and random motion

We study infinite weighted graphs with view to \textquotedblleft limits at infinity,\textquotedblright or boundaries at infinity. Examples of such weighted graphs arise in infinite (in practice, that means \textquotedblleft very\textquotedblright large) networks of resistors, or in statistical mechanics models for classical or quantum systems. But more generally our analysis includes reproducing kernel Hilbert spaces and associated operators on them. If $X$ is some infinite set of vertices or nodes, in applications the essential ingredient going into the definition is a reproducing kernel Hilbert space; it measures the differences of functions on $X$ evaluated on pairs of points in $X$. And the Hilbert norm-squared in $\mathcal{H}(X)$ will represent a suitable measure of energy. Associated unbounded operators will define a notion or dissipation, it can be a graph Laplacian, or a more abstract unbounded Hermitian operator defined from the reproducing kernel Hilbert space under study. We prove that there are two closed subspaces in reproducing kernel Hilbert space $\mathcal{H}(X)$ which measure quantitative notions of limits at infinity in $X$, one generalizes finite-energy harmonic functions in $\mathcal{H}(X)$, and the other a deficiency index of a natural operator in $\mathcal{H}(X)$ associated directly with the diffusion. We establish these results in the abstract, and we offer examples and applications. Our results are related to, but different from, potential theoretic notions of \textquotedblleft boundaries\textquotedblright in more standard random walk models. Comparisons are made.Comment: 38 pages, 4 tables, 3 figure

Torsion, Dirac Field, Dark Matter and Dark Radiation

The role of torsion and a scalar field $\phi$ in gravitation, especially, in the presence of a Dirac field in the background of a particular class of the Riemann-Cartan geometry is considered here. Recently, a Lagrangian density with Lagrange multipliers has been proposed by the author which has been obtained by picking some particular terms from the SO(4,1) Pontryagin density, where the scalar field $\phi$ causes the de Sitter connection to have the proper dimension of a gauge field. In this article the scalar field has been linked to the dimension of the Dirac field. Here we get the field equations for the Dirac field and the scalar field in such a way that both of them appear to be mutually non-interacting. In this scenario the scalar field appears to be a natural candidate for the dark matter and the dark radiation

The Spatial Averaging Limit of Covariant Macroscopic Gravity - Scalar Corrections to the Cosmological Equations

It is known that any explicit averaging scheme of the type essential for describing the large scale behaviour of the Universe, must necessarily yield corrections to the Einstein equations applied in the Cosmological setting. The question of whether or not the resulting corrections to the Einstein equations are significant, is still a subject of debate, partly due to possible ambiguities in the averaging schemes available. In particular, it has been argued in the literature that the effects of averaging could be gauge artifacts. We apply the formalism of Zalaletdinov's Macroscopic Gravity (MG) which is a fully covariant and nonperturbative averaging scheme, in an attempt to construct gauge independent corrections to the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) equations. We find that whereas one cannot escape the problem of dependence on \emph{one} gauge choice -- which is inherent in the assumption of large scale homogeneity and isotropy -- it is however possible to construct \emph{spacetime scalar} corrections to the standard FLRW equations. This partially addresses the criticism concerning the corrections being gauge artifacts. For a particular initial choice of gauge which simplifies the formalism, we explicitly construct these scalars in terms of the underlying inhomogeneous geometry, and incidentally demonstrate that the formal structure of the corrections with this gauge choice is identical to that of analogous corrections derived by Buchert in the context of spatial averaging of scalars.Comment: 18 pages, no figures, revtex4; v2 - minor clarifications added; v3 - minor changes in presentation to improve clarity, reference added, to appear in Phys. Rev.

Superconductivity due to fluctuating loop currents

Orbital magnetism and the loop currents (LC) that accompany it have been proposed to emerge in many systems, including cuprates, iridates, and kagome superconductors. In the case of cuprates, LCs have been put forward as the driving force behind the pseudogap, strange-metal behavior, and $d_{x^2-y^2}$-wave superconductivity. Here, we investigate whether fluctuating intra-unit-cell loop currents can cause unconventional superconductivity. For odd-parity LCs, we find that they are strongly repulsive in all pairing channels near the underlying quantum-critical point (QCP). For even-parity LCs, their fluctuations do give rise to unconventional pairing. However, this pairing is not amplified in the vicinity of the QCP, in sharp contrast to other known cases of pairing mediated by intra-unit-cell order parameters, such as spin-magnetic, nematic, or ferroelectric ones. Applying our formalism to the cuprates, we conclude that pairing mediated by fluctuating intra-unit-cell LCs is unlikely to yield $d_{x^2-y^2}$-wave superconductivity. We also show that loop currents, if relevant for the cuprates, must vary between unit cells and break translation symmetry.Comment: 12 pages, 7 figure