Radiation recoil from highly distorted black holes

We present results from numerical evolutions of single black holes distorted by axisymmetric, but equatorially asymmetric, gravitational (Brill) waves. Net radiated energies, apparent horizon embeddings, and recoil velocities are shown for a range of Brill wave parameters, including both even and odd parity distortions of Schwarzschild black holes. We find that a wave packet initially concentrated on the black hole throat, a likely model also for highly asymmetric stellar collapse and late stage binary mergers, can generate a maximum recoil velocity of about 150 (23) km/sec for even (odd) parity perturbations, significantly less than that required to eject black holes from galactic cores.Comment: 15 pages, 8 figure

Berezinians, Exterior Powers and Recurrent Sequences

We study power expansions of the characteristic function of a linear operator $A$ in a $p|q$-dimensional superspace $V$. We show that traces of exterior powers of $A$ satisfy universal recurrence relations of period $q$. `Underlying' recurrence relations hold in the Grothendieck ring of representations of \GL(V). They are expressed by vanishing of certain Hankel determinants of order $q+1$ in this ring, which generalizes the vanishing of sufficiently high exterior powers of an ordinary vector space. In particular, this allows to explicitly express the Berezinian of an operator as a rational function of traces. We analyze the Cayley--Hamilton identity in a superspace. Using the geometric meaning of the Berezinian we also give a simple formulation of the analog of Cramer's rule.Comment: 35 pages. LaTeX 2e. New version: paper substantially reworked and expanded, new results include

Precise Tight-binding Description of the Band Structure of MgB2

We present a careful recasting of first-principles band structure calculations for MgB2 in a non-orthogonal sp-tight-binding (TB) basis. Our TB results almost exactly reproduce our full potential linearized augmented plane wave results for the energy bands, the densities of states and the total energies. Our procedure generates transferable Slater-Koster parameters which should be useful for other studies of this important material.Comment: REVTEX, 2 Encapsulated PostScript Figure

The European Commission’s Green Deal is an opportunity to rethink harmful practices of research and innovation policy

The European Union’s Green Deal and associated policies, aspiring to long-term environmental sustainability, now require economic activities to ‘do no significant harm’ to EU environmental objectives. The way the European Commission is enacting the do no significant harm principle relies on quantitative tools that try to identify harm and adjudicate its significance. A reliance on established technical approaches to assessing such questions ignores the high levels of imprecision, ambiguity, and uncertainty—levels often in flux—characterizing the social contexts in which harms emerge. Indeed, harm, and its significance, are relational, not absolute. A better approach would thus be to acknowledge the relational nature of harm and develop broad capabilities to engage and ‘stay with’ the harm. We use the case of European research and innovation activities to expose the relational nature of harm, and explore an alternative and potentially more productive approach that departs from attempts to unilaterally or uniformly claim to know or adjudicate what is or is not significantly harmful. In closing, we outline three ways research and innovation policy-makers might experiment with reconfiguring scientific and technological systems and practices to better address the significant harms borne by people, other-than-human beings, and ecosystems. Merit, Expertise and Measuremen

The nil Hecke ring and singularity of Schubert varieties

We give a criterion for smoothness of a point in any Schubert variety in any G/B in terms of the nil Hecke ring.Comment: AMSTE

Weak lensing, dark matter and dark energy

Weak gravitational lensing is rapidly becoming one of the principal probes of dark matter and dark energy in the universe. In this brief review we outline how weak lensing helps determine the structure of dark matter halos, measure the expansion rate of the universe, and distinguish between modified gravity and dark energy explanations for the acceleration of the universe. We also discuss requirements on the control of systematic errors so that the systematics do not appreciably degrade the power of weak lensing as a cosmological probe.Comment: Invited review article for the GRG special issue on gravitational lensing (P. Jetzer, Y. Mellier and V. Perlick Eds.). V3: subsection on three-point function and some references added. Matches the published versio

Tunneling of quantum rotobreathers

We analyze the quantum properties of a system consisting of two nonlinearly coupled pendula. This non-integrable system exhibits two different symmetries: a permutational symmetry (permutation of the pendula) and another one related to the reversal of the total momentum of the system. Each of these symmetries is responsible for the existence of two kinds of quasi-degenerated states. At sufficiently high energy, pairs of symmetry-related states glue together to form quadruplets. We show that, starting from the anti-continuous limit, particular quadruplets allow us to construct quantum states whose properties are very similar to those of classical rotobreathers. By diagonalizing numerically the quantum Hamiltonian, we investigate their properties and show that such states are able to store the main part of the total energy on one of the pendula. Contrary to the classical situation, the coupling between pendula necessarily introduces a periodic exchange of energy between them with a frequency which is proportional to the energy splitting between quasi-degenerated states related to the permutation symmetry. This splitting may remain very small as the coupling strength increases and is a decreasing function of the pair energy. The energy may be therefore stored in one pendulum during a time period very long as compared to the inverse of the internal rotobreather frequency.Comment: 20 pages, 11 figures, REVTeX4 styl