Exotic Smoothness and Quantum Gravity

Since the first work on exotic smoothness in physics, it was folklore to assume a direct influence of exotic smoothness to quantum gravity. Thus, the negative result of Duston (arXiv:0911.4068) was a surprise. A closer look into the semi-classical approach uncovered the implicit assumption of a close connection between geometry and smoothness structure. But both structures, geometry and smoothness, are independent of each other. In this paper we calculate the "smoothness structure" part of the path integral in quantum gravity assuming that the "sum over geometries" is already given. For that purpose we use the knot surgery of Fintushel and Stern applied to the class E(n) of elliptic surfaces. We mainly focus our attention to the K3 surfaces E(2). Then we assume that every exotic smoothness structure of the K3 surface can be generated by knot or link surgery a la Fintushel and Stern. The results are applied to the calculation of expectation values. Here we discuss the two observables, volume and Wilson loop, for the construction of an exotic 4-manifold using the knot $5_{2}$ and the Whitehead link $Wh$. By using Mostow rigidity, we obtain a topological contribution to the expectation value of the volume. Furthermore we obtain a justification of area quantization.Comment: 16 pages, 1 Figure, 1 Table subm. Class. Quant. Grav

The modification of the energy spectrum of charged particles by exotic open 4-smoothness via superstring theory

In this paper we present a model where the modified Landau-like levels of charged particles in a magnetic field are determined due to the modified smoothness of $\mathbb{R}^{4}$ as underlying structure of the Minkowski spacetime. Then the standard smoothness of $\mathbb{R}^{4}$ is shifted to the exotic $\mathbb{R}_{k}^{4}$, $k=2p$, $p=1,2...$. This is achieved by superstring theory using gravitational backreaction induced from a strong, almost constant magnetic field on standard $\mathbb{R}^{4}$. The exact string background containing flat $\mathbb{R}^{4}$ is replaced consistently by the curved geometry of $SU(2)_{k}\times\mathbb{R}$ as part of the modified exact backgrounds. This corresponds to the change of smoothness on $\mathbb{R}^{4}$ from the standard $\mathbb{R}^{4}$ to some exotic $\mathbb{R}_{k}^{4}$. The calculations of the spectra are using the CFT marginal deformations and Wess-Zumino-Witten (WZW) models. The marginal deformations capture the effects of the magnetic field as well as its gravitational backreactions. The spectra depend on even level $k$ of WZW on SU(2). At the same time the WZ term as element of $H^{3}(SU(2),\mathbb{R})$ determines also the exotic smooth $\mathbb{R}_{k}^{4}$. As the consequence we obtain a non-zero mass-gap emerges in the spectrum induced from the presence of an exotic $\mathbb{R}_{k}^{4}$.Comment: 11 pages, Revtex4-1, will appear IJGMMP Vol. 50(1), 201

Possible Gravitational Microlensing Events in the Optical Lightcurve of Active Galaxy S5 0716+714

A well-known active galaxy of the blazar type, S5 0716+714, is characterized by a particularly high variability duty cycle on short-time scales at optical frequencies. As such, the source was subjected to numerous monitoring programs, including both ground-based as well as space-borne telescopes. On closer inspection of the most recent accumulation of the data provided by the Transiting Exoplanet Survey Satellite, we have noticed several conspicuous events with `volcano-like' symmetric shape, lasting all for several hours, which closely resemble the achromatic events detected with the previous Whole Earth Blazar Telescope campaigns targeting the source. We propose that those peculiar features could be due to the gravitational micro-lensing of the innermost segments of the precessing jet in the system, by a binary lens. We study the magnification pattern of the lens with the inverse-ray shooting method, and the source trajectory parameters with the Python package MuLensModel. In this way, we were able to fit successfully all the selected events with a single lens, adjusting slightly only the source trajectory parameters for each lensing event. Based on the fit results, we postulate the presence of a massive binary lens, containing an intermediate-mass black hole, possibly even a super-massive one, and a much less massive companion (by a factor of $\lesssim 0.01$), located within the host galaxy of the blazar, most likely the central kiloparsec region. We discuss the major physical implications of the proposed scenario regarding the quest for the intermediate-mass and dual supermassive black holes in active galaxies.Comment: accepted for publication in the Astrophysical Journa

Synthesis and characterisation of coating polyurethane cationomers containing fluorine built-in hard urethane segments

Polyurethane cationomers were synthesised in the reaction of 4,4’-methylenebis(phenyl isocyanate) with polyoxyethylene glycol (M = 2,000) or poly(tetrafluoroethyleneoxide-co-difluoromethylene oxide) α,ω-diisocyanate and N-methyl diethanolamine. Amine segments were built-in to the urethane-isocyanate prepolymer in the reaction with 1-bromobutane or formic acid, and then they were converted to alkylammonium cations. The obtained isocyanate prepolymers were then extended in the aqueous medium that yielded stable aqueous dispersions which were applied on the surfaces of test poly(tetrafluoroethylene) plates. After evaporation of water, the dispersions formed thin polymer coatings. 1H, 13C NMR and IR spectral methods were employed to confirm chemical structures of synthesised cationomers. Based on 1H NMR and IR spectra, the factors κ and α were calculated, which represented the polarity level of the obtained cationomers. The DSC, wide angle X-ray scattering and atom force microscopy methods were employed for the microstructural assessment of the obtained materials. Changes were discussed in the surface free energy and its components, as calculated independently according to the method suggested by van Oss–Good, in relation to chemical and physical structures of cationomers as well as morphology of coating surfaces obtained from those cationomers. Fluorine incorporated into cationomers (about 30%) contributed to lower surface free energy values, down to about 15 mJ/m2. That was caused by gradual weakening of long-range interactions within which the highest share is taken by dispersion interactions

Topological quantum D-branes and wild embeddings from exotic smooth R^4

This is the next step of uncovering the relation between string theory and exotic smooth R^4. Exotic smoothness of R^4 is correlated with D6 brane charges in IIA string theory. We construct wild embeddings of spheres and relate them to a class of topological quantum Dp-branes as well to KK theory. These branes emerge when there are non-trivial NS-NS H-fluxes where the topological classes are determined by wild embeddings S^2 -> S^3. Then wild embeddings of higher dimensional $p$-complexes into S^n correspond to Dp-branes. These wild embeddings as constructed by using gropes are basic objects to understand exotic smoothness as well Casson handles. Next we build C*-algebras corresponding to the embeddings. Finally we consider topological quantum D-branes as those which emerge from wild embeddings in question. We construct an action for these quantum D-branes and show that the classical limit agrees with the Born-Infeld action such that flat branes = usual embeddings.Comment: 18 pages, 1 figur

Diversity of vertebrate remains from the Lower Gogolin Beds (Anisian) of southern Poland

Middle Triassic (Muschelkalk) limestones and dolostones of southern Poland contain vertebrate remains, which can be used for palaeoecological and palaeogeographical analyses. The results presented concern vertebrate remains uncovered at four localities in Upper Silesia and one on Opole Silesia, a region representing the south-eastern margin of the Germanic Basin in Middle Triassic times. The most abundant remains in this assemblage are fish remains, comprising mostly actinopterygian teeth and scales. Chondrichthyan and sauropsid remains are less common. Reptilian finds include vertebrae, teeth and fragments of long bones, belonging to aquatic or semi-aquatic reptiles, such as nothosaurids, pachypleusorosaurids, and ichthyosaurids. Also, coprolites of possibly durophagous and predacious reptiles occur. In the stratigraphic column of Mikołów, actinopterygian remains are the most numerous and no distinct changes of the taxonomic composition occur. Although this assemblage differs from those described at other localities (Ząbkowice with numerous chondrichthyans, Żyglin, and Płaza with common sauropsid fossils), sampling bias has to be considered