Extreme recoils: impact on the detection of gravitational waves from massive black hole binaries

Recent numerical simulations of coalescences of highly spinning massive black hole binaries (MBHBs) suggest that the remnant can suffer a recoil velocity of the order of few thousands km/s. We study here, by means of dedicated simulations of black holes build--up, how such extreme recoils could affect the cosmological coalescence rate of MBHBs, placing a robust lower limit for the predicted number of gravitational wave (GW) sources detectable by future space--borne missions (such as LISA). We consider two main routes for black hole formation: one where seeds are light remnants of Population III stars (~10^2 \msun), and one where seeds are much heavier (>~10^4 \msun), formed via the direct gas collapse in primordial nuclear disks. We find that extreme recoil velocities do not compromise the efficient MBHB detection by LISA. If seeds are already massive and/or relatively rare, the detection rate is reduced by only ~15%. The number of detections drops substantially (by ~60%) if seeds are instead light and abundant, but in this case the number of predicted coalescences is so high that at least ~10 sources in a three year observation are guaranteed.Comment: 5 pages, 4 figures, replaced with final versio

N electrons in a quantum dot: Two-point Pade approximants

We present analytic estimates for the energy levels of N electrons (N = 2 - 5) in a two-dimensional parabolic quantum dot. A magnetic field is applied perpendicularly to the confinement plane. The relevant scaled energy is shown to be a smooth function of the parameter \beta=(effective Rydberg/effective dot energy)^{1/6}. Two-point Pade approximants are obtained from the series expansions of the energy near the oscillator ($\beta\to 0$) and Wigner ($\beta\to\infty$) limits. The approximants are expected to work with an error not greater than 2.5% in the entire interval $0\le\beta < \infty$.Comment: 27 pages. LaTeX. 6 figures not include

Dirac Quasinormal Modes of New Type Black Holes in New Massive Gravity

We study new type black holes in three-dimensional New Massive Gravity and we calculate analytically the quasinormal modes for fermionic perturbations for some special cases. Then, we show that for these cases the new type black holes are stable under fermionic field perturbations.Comment: improved version. arXiv admin note: text overlap with arXiv:1306.5974, arXiv:1404.317

Two and three electrons in a quantum dot: 1/|J| - expansion

We consider systems of two and three electrons in a two-dimensional parabolic quantum dot. A magnetic field is applied perpendicularly to the electron plane of motion. We show that the energy levels corresponding to states with high angular momentum, J, and a low number of vibrational quanta may be systematically computed as power series in 1/|J|. These states are relevant in the high-B limit.Comment: LaTeX, 15 pages,6 postscript figure

Boundary dynamics of asymptotically flat 3D gravity coupled to higher spin fields

We construct a two-dimensional action principle invariant under a spin-three extension of BMS$_3$ group. Such a theory is obtained through a reduction of Chern-Simons action with a boundary. This procedure is carried out by imposing a set of boundary conditions obtained from asymptotically flat spacetimes in three dimensions. When implementing part of this set, we obtain an analog of chiral WZW model based on a contraction of $sl(3,\mathbb{R}) \times sl(3,\mathbb{R})$. The remaining part of the boundary conditions imposes constraints on the conserved currents of the model, which allows to further reduce the action principle. It is shown that a sector of this latter theory is related to a flat limit of Toda theory.Comment: 16 pages, no figure

On quark-lepton complementarity

Recent measurements of the neutrino solar mixing angle and the Cabibbo angle satisfy the empirical relation theta_{sol} + theta_{C} ~ 45^{o}. This relation suggests the existence of a correlation between the mixing matrices of leptons and quarks, the so called quark-lepton complementarity. Here, we examine the possibility that this correlation originates in the strong hierarchy in the mass spectra of quarks and charged leptons, and the seesaw mechanism that gives mass to the Majorana neutrinos. In a unified treatment of quarks and leptons in which the mass matrices of all fermions have a similar Fritzsch texture, we calculate the mixing matrices V_{CKM} and U_{MNSP} as functions of quark and lepton masses and only two free parameters, in very good agreement with the latest experimental values on masses and mixings. Three essential ingredients to explain the quark-lepton complementarity relation are identified: the strong hierarchy in the mass spectra of quarks and charged leptons, the normal seesaw mechanism and the assumption of maximal CP violation in the lepton sector.Comment: 6 pages, to appear in "Particles and fields: Xth Mexican Workshop on Particles and Fields" (Morelia, Mich. Mexico, November 6-12, 2005), Eds. A. Bashir and L. Villasenor, AIP Conference proceedings (2006