Foliations invariant by rational maps

We give a classification of pairs (F, f) where F is a holomorphic foliation on a projective surface and f is a non-invertible dominant rational map preserving F. We prove that both the map and the foliation are integrable in a suitable sense.Comment: 17 pages. To appear in Math. Zeitshrift

Probing the Effects of Lorentz-Symmetry Violating Chern-Simons and Ricci-Cotton Terms in Higher Derivative Gravity

The combined effects of the Lorentz-symmetry violating Chern-Simons and Ricci-Cotton actions are investigated for the Einstein-Hilbert gravity in the second order formalism modified by higher derivative terms, and their consequences on the spectrum of excitations are analyzed. We follow the lines of previous works and build up an orthonormal basis of operators that splits the fundamental fields according to their individual degrees of freedom. With this new basis, the attainment of the propagators is remarkably simplified and the identification of the physical and unphysical modes gets a new insight. Our conclusion is that the only tachyon- and ghost-free model is the Einstein-Hilbert action added up by the Chern-Simons term with a time-like vector of the type $v^{\mu} = (\mu,\vec{0})$. Spectral consistency imposes taht the Ricci-Cotton term must be switched off. We then infer that gravity with Lorentz-symmetry violation imposes a drastically different constraint on the background if compared to usual gauge theories whenever conditions for suppression of tachyons and ghosts are required.Comment: 15 pages. It coincides with the version published in Phys. Rev.

Conformal and gauge invariant spin-2 field equations

Using an approach based on the Casimir operators of the de Sitter group, the conformal invariant equations for a fundamental spin-2 field are obtained, and their consistency discussed. It is shown that, only when the spin-2 field is interpreted as a 1-form assuming values in the Lie algebra of the translation group, rather than a symmetric second-rank tensor, the field equation is both conformal and gauge invariant.Comment: 12 pages, no figures; accepted for publication in Gravitation & Cosmolog

Chemical analysis of giant stars in the young open cluster NGC 3114

Context: Open clusters are very useful targets for examining possible trends in galactocentric distance and age, especially when young and old open clusters are compared. Aims: We carried out a detailed spectroscopic analysis to derive the chemical composition of seven red giants in the young open cluster NGC 3114. Abundances of C, N, O, Li, Na, Mg, Al, Ca, Si, Ti, Ni, Cr, Y, Zr, La, Ce, and Nd were obtained, as well as the carbon isotopic ratio. Methods: The atmospheric parameters of the studied stars and their chemical abundances were determined using high-resolution optical spectroscopy. We employed the local-thermodynamic-equilibrium model atmospheres of Kurucz and the spectral analysis code MOOG. The abundances of the light elements were derived using the spectral synthesis technique. Results: We found that NGC 3114 has a mean metallicity of [Fe/H] = -0.01+/-0.03. The isochrone fit yielded a turn-off mass of 4.2 Msun. The [N/C] ratio is in good agreement with the models predicted by first dredge-up. We found that two stars, HD 87479 and HD 304864, have high rotational velocities of 15.0 km/s and 11.0 km/s; HD 87526 is a halo star and is not a member of NGC 3114. Conclusions: The carbon and nitrogen abundance in NGC 3114 agree with the field and cluster giants. The oxygen abundance in NGC 3114 is lower compared to the field giants. The [O/Fe] ratio is similar to the giants in young clusters. We detected sodium enrichment in the analyzed cluster giants. As far as the other elements are concerned, their [X/Fe] ratios follow the same trend seen in giants with the same metallicity.Comment: 17 pages, 9 figures, 10 tables; accepted for publication in A&

Resonant tunneling through protected quantum dots at phosphorene edges

We theoretically investigate phosphorene zigzag nanorribons as a platform for constriction engineering. In the presence of a constriction at the upper edge, quantum confinement of edge protected states reveals resonant tunnelling Breit-Wigner transmission peaks, if the upper edge is uncoupled to the lower edge. Coupling between edges in thin constrictions gives rise to Fano-like and anti-resonances in the transmission spectrum of the system.Comment: 8 pages,7 figure

Phantom Accretion by Black Holes and the Generalized Second Law of Thermodynamics

The accretion of a phantom fluid with non-zero chemical potential by black holes is discussed with basis on the Generalized Second Law of thermodynamics. For phantom fluids with positive temperature and negative chemical potential we demonstrate that the accretion process is possible, and that the condition guaranteeing the positiveness of the phantom fluid entropy coincides with the one required by Generalized Second Law. In particular, this result provides a complementary confirmation that cosmological phantom fluids do not need to have negative temperatures