Asymptotically Stationary and Static Space-times and Shear-free Null Geodesic Congruences

In classical electromagnetic theory, one formally defines the complex dipole moment (the electric plus 'i' magnetic dipole) and then computes (and defines) the complex center of charge by transforming to a complex frame where the complex dipole moment vanishes. Analogously in asymptotically flat space-times it has been shown that one can determine the complex center of mass by transforming the complex gravitational dipole (mass dipole plus 'i' angular momentum) (via an asymptotic tetrad trasnformation) to a frame where the complex dipole vanishes. We apply this procedure to such space-times which are asymptotically stationary or static, and observe that the calculations can be performed exactly, without any use of the approximation schemes which must be employed in general. In particular, we are able to exactly calculate complex center of mass and charge world-lines for such space-times, and - as a special case - when these two complex world-lines coincide, we recover the Dirac value of the gyromagnetic ratio.Comment: 11 page

The Generalized Good Cut Equation

The properties of null geodesic congruences (NGCs) in Lorentzian manifolds are a topic of considerable importance. More specifically NGCs with the special property of being shear-free or asymptotically shear-free (as either infinity or a horizon is approached) have received a great deal of recent attention for a variety of reasons. Such congruences are most easily studied via solutions to what has been referred to as the 'good cut equation' or the 'generalization good cut equation'. It is the purpose of this note to study these equations and show their relationship to each other. In particular we show how they all have a four complex dimensional manifold (known as H-space, or in a special case as complex Minkowski space) as a solution space.Comment: 12 page

Color Fields on the Light-Shell

We study the classical color radiation from very high energy collisions that produce colored particles. In the extreme high energy limit, the classical color fields are confined to a light-shell expanding at $c$ and are associated with a non-linear $\sigma$-model on the 2D light-shell with specific symmetry breaking terms. We argue that the quantum version of this picture exhibits asymptotic freedom and may be a useful starting point for an effective light-shell theory of the structure between the jets at a very high energy collider.Comment: 11 pages, no figure

The Real Meaning of Complex Minkowski-Space World-Lines

In connection with the study of shear-free null geodesics in Minkowski space, we investigate the real geometric effects in real Minkowski space that are induced by and associated with complex world-lines in complex Minkowski space. It was already known, in a formal manner, that complex analytic curves in complex Minkowski space induce shear-free null geodesic congruences. Here we look at the direct geometric connections of the complex line and the real structures. Among other items, we show, in particular, how a complex world-line projects into the real Minkowski space in the form of a real shear-free null geodesic congruence.Comment: 16 page

VLT/MUSE view of the highly ionized outflow cones in the nearby starburst ESO338-IG04

The Ly$\alpha$ line is an important diagnostic for star formation at high redshift, but interpreting its flux and line profile is difficult because of the resonance nature of Ly$\alpha$. Trends between the escape of Ly$\alpha$ photons and dust and properties of the interstellar medium (ISM) have been found, but detailed comparisons between Ly$\alpha$ emission and the properties of the gas in local high-redshift analogs are vital for understanding the relation between Ly$\alpha$ emission and galaxy properties. For the first time, we can directly infer the properties of the ionized gas at the same location and similar spatial scales of the extended Ly$\alpha$ halo around ESO 338-IG04. We obtained VLT/MUSE integral field spectra. We used ionization parameter mapping of the [SII]/[OIII] line ratio and the kinematics of H$\alpha$ to study the ionization state and kinematics of the ISM of ESO338-IG04. The velocity map reveals two outflows. The entire central area of the galaxy is highly ionized by photons leaking from the HII regions around the youngest star clusters. Three highly ionized cones have been identified, of which one is associated with an outflow. We propose a scenario where the outflows are created by mechanical feedback of the older clusters, while the highly ionized gas is caused by the hard ionizing photons emitted by the youngest clusters. A comparison with the Ly$\alpha$ map shows that the (approximately bipolar) asymmetries observed in the Ly$\alpha$ emission are consistent with the base of the outflows detected in H$\alpha$. No clear correlation with the ionization cones is found. The mechanical and ionization feedback of star clusters significantly changes the state of the ISM by creating ionized cones and outflows. The comparison with Ly$\alpha$ suggests that especially the outflows could facilitate the escape of Ly$\alpha$ photons [Abridged].Comment: Accepted for publication in A&A Letters, 4 pages, 2 figure

Inhibition of phosphoinositide 3-kinase/protein kinase B signaling hampers the vasopressin-dependent stimulation of myogenic differentiation

Arginine-vasopressin (AVP) promotes muscle differentiation, hypertrophy, and regeneration through the combined activation of the calcineurin and Calcium/Calmodulin-dependent Protein Kinase (CaMK) pathways. The AVP system is impaired in several neuromuscular diseases, suggesting that AVP may act as a physiological factor in skeletal muscle. Since the Phosphoinositide 3-kinases/Protein Kinase B/mammalian Target Of Rapamycin (PI3K/Akt/mTOR) signaling plays a significant role in regulating muscle mass, we evaluated its role in the AVP myogenic effect. In L6 cells AKT1 expression was knocked down, and the AVP-dependent expression of mTOR and Forkhead box O3 (FoxO) was analyzed by Western blotting. The effect of the PI3K inhibitor LY294002 was evaluated by cellular and molecular techniques. Akt knockdown hampered the AVP-dependent mTOR expression while increased the levels of FoxO transcription factor. LY294002 treatment inhibited the AVP-dependent expression of Myocyte Enhancer Factor-2 (MEF2) and myogenin and prevented the nuclear translocation of MEF2. LY294002 also repressed the AVP-dependent nuclear export of histone deacetylase 4 (HDAC4) interfering with the formation of multifactorial complexes on the myogenin promoter. We demonstrate that the PI3K/Akt pathway is essential for the full myogenic effect of AVP and that, by targeting this pathway, one may highlight novel strategies to counteract muscle wasting in aging or neuromuscular disorders

Super star cluster feedback driving ionization, shocks and outflows in the halo of the nearby starburst ESO 338-IG04

Stellar feedback strongly affects the interstellar medium (ISM) of galaxies. Stellar feedback in the first galaxies likely plays a major role in enabling the escape of LyC photons, which contribute to the re-ionization of the Universe. Nearby starburst galaxies serve as local analogues allowing for a spatially resolved assessment of the feedback processes in these galaxies. We characterize the feedback effects from the star clusters in the local high-redshift analogue ESO 338-IG04 on the ISM and compare the results with the properties of the most massive clusters. We use high quality VLT/MUSE optical integral field data to derive the physical properties of the ISM such as ionization, density, shocks, and perform new fitting of the spectral energy distributions of the brightest clusters in ESO 338-IG04 from HST imaging. ESO 338-IG04 has a large ionized halo which we detect to a distance of 9 kpc. We identify 4 Wolf-Rayet (WR) clusters based on the blue and red WR bump. We follow previously identified ionization cones and find that the ionization of the halo increases with distance. Analysis of the galaxy kinematics shows two complex outflows driven by the numerous young clusters in the galaxy. We find a ring of shocked emission traced by an enhanced [OI]/H$\alpha$ ratio surrounding the starburst and at the end of the outflow. Finally we detect nitrogen enriched gas associated with the outflow, likely caused by the WR stars in the massive star clusters. Photo-ionization dominates the central starburst and sets the ionization structure of the entire halo, resulting in a density bounded halo, facilitating the escape of LyC photons. Outside the central starburst, shocks triggered by an expanding super bubble become important. The shocks at the end of the outflow suggest interaction between the hot outflowing material and the more quiescent halo gas.Comment: Accepted for publication in Astronomy and Astrophysics, 22 pages, 15 figure

Diagonal classes and the Bloch–Kato conjecture

The aim of this note is twofold. Firstly, we prove an explicit reciprocity law for certain diagonal classes in the \ub4etale cohomology of the triple product of a modular curve, stated in [8] and used there as a crucial ingredient in the proof of the main results. Secondly, we apply the aforementioned reciprocity law to address the rank-zero case of the equivariant Bloch\u2013Kato conjecture for the self-dual motive of an elliptic newform of weight k > 2. In the special case k = 2, our result gives a self-contained and simpler proof of the main result of [15]