Electronic properties of curved few-layers graphene : a geometrical approach.

We show the presence of non-relativistic L?vy-Leblond fermions in flat three- and four-layers graphene with AB stacking, extending the results obtained in Cariglia et al. 2017 for bilayer graphene. When the layer is curved we obtain a set of equations for Galilean fermions that are a variation of those of L?vy-Leblond with a well defined combination of pseudospin, and that admit L?vy-Leblond spinors as solutions in an approriate limit. The local energy of such Galilean fermions is sensitive to the intrinsic curvature of the surface. We discuss the relationship between two-dimensional pseudospin, labelling layer degrees of freedom, and the different energy bands. For L?vy-Leblond fermions, an interpretation is given in terms of massless fermions in an effective 4D spacetime, and in this case the pseudospin is related to four dimensional chirality. A non-zero energy band gap between conduction and valence electronic bands is obtained for surfaces with positive curvature

Sufficient condition for Blackhole formation in spherical gravitational collapse

A sufficient condition for the validity of Cosmic Censorship in spherical gravitational collapse is formulated and proved. The condition relies on an attractive mathematical property of the apparent horizon, which holds if ''minimal'' requirements of physical reasonableness are satisfied by the matter model.Comment: 5 pages, LaTeX2

ACCRETION DISK LUMINOSITY FOR BLACK HOLES SURROUNDED BY DARK MATTER WITH ANISOTROPIC PRESSURE

We investigate the luminosity of the accretion disk for a static black hole surrounded by dark matter with anisotropic pressure. We calculate all basic orbital parameters of test particles in the accretion disk, such as angular velocity, angular momentum, energy and radius of the innermost circular stable orbit as functions of the dark matter density, radial pressure and anisotropic param eter, which establishes the relationship between the radial and tangential pressures. We show that the presence of dark matter with anisotropic pressure makes a noticeable difference in the geometry around a Schwarzschild black hole, affecting the radiative flux, differential luminosity and spectral luminosity of the accretion disk