We examine magnetorotationally driven supernovae as sources of r-process elements in the early Galaxy. On the basis of thermodynamic histories of tracer particles from a three-dimensional magnetohydrodynamical core-collapse supernova model with approximated neutrino transport, we perform nucleosynthesis calculations with and without considering the effects of neutrino absorption reactions on the electron fraction (Y e ) during post-processing. We find that the peak distribution of Y e in the ejecta is shifted from ∼ 0.15 to ∼ 0.17 and broadened toward higher Y e due to neutrino absorption. Nevertheless, in both cases the second and third peaks of the solar r-process element distribution can be well reproduced. The rare progenitor configuration that was used here, characterized by a high rotation rate and a large magnetic field necessary for the formation of bipolar jets, could naturally provide a site for the strong r-process in agreement with observations of the early galactic chemical evolution.

Non-continuous "jumps" of Apparent Horizons occur generically in 3+1 (binary) black hole evolutions. The dynamical trapping horizon framework suggests a spacetime picture in which these "Apparent Horizon jumps" are understood as spatial cuts of a single spacetime hypersurface foliated by (compact) marginally outer trapped surfaces. We present here some work in progress which makes use of uni-parametric sequences of (axisymmetric) binary black hole initial data for exploring the plausibility of this spacetime picture. The modelling of Einstein evolutions by sequences of initial data has proved to be a successful methodological tool in other settings for the understanding of certain qualitative features of evolutions in restricted physical regimes. Keywords: trapping and dynamical horizons, black hole mergers, numerical relativity PACS: 04.70.Bw, 04.25.dg, 02.70.HmProblem and antecedents. We aim here at gaining some insight into the understanding of non-continuous Apparent Ronzonjumps occurring generically in 3+1 evolutions of black hole spacetimes, with a focus on the binary case. We look at this problem from the perspective of a geometric quasi-local approach to black holes, namely the dynamical trapping horizons introduced by Hayward and Ashtekar & Krishnan (cf.[1] for a recent review). This framework suggests a spacetime picture in which these Apparent Horizon jumps actually correspond to different (non-connected) spatial cuts of a unique underlying smooth hypersurface ^ foliated by (compact) marginally outer trapped surfaces, when ^ is sliced by a given spacelike hypersurface E. Our goal here is to assess this qualitative spacetime picture by means of some specific numerical implementations.The setting of the dynamical trapping horizon framework is the quasi-local characterization of a black hole in terms of a trapped region. The latter is built on the notion of trapped surface, a closed surface on which the expansions associated with outgoing ^+ and ingoing fr null congruences are negative: 0+ < 0 and 0_ < 0, respectively. The black hole horizon is then modelled as a worldtube ^ of marginally outer trapped surfaces (MOTS), i.e. 0+ = 0. Additional geometric conditions are needed for ^ to fulfill the expected physical properties of the horizon, namely: a) a future condition, 0_ < 0, crucial for deriving an area growth law; and b) an outer condition 5^-9+ < 0, meaning that when moving inwards the horizon we enter into the trapped region. Under the null energy condition, horizon J^ is either a spacelike or null hypersurface. From a 3+1 perspective, we consider the intersections ^^ of ^ with slices {Lt} in a 3+1 spacetime foliation. A given E^ can multiply intersect ^ giving rise to Apparent Horizon jumps CPl 122, Physics and Mathematics of Gravitation, edited by K. E. Kunze, M. Mars, and M. A. Vazquez-Mozo O 2009 American Institute of Physics 978-0-7354-0658-2/09/$25.00 308

We present a numerical work aiming at the computation of excised initial data for black hole spacetimes in full general relativity, using Dirac gauge in the context of a constrained formalism for the Einstein equations. Introducing the isolated horizon formalism for black hole excision, we especially solve the conformal metric part of the equations, and assess the boundary condition problem for it. In the stationary single black hole case, we present and justify a no-boundary treatment on the black hole horizon. We compare the data obtained with the well-known analytic Kerr solution in Kerr-Schild coordinates, and assess the widely used conformally flat approximation for simulating axisymmetric black hole spacetimes. Our method shows good concordance on physical and geometrical issues, with the particular application of the isolated horizon multipolar analysis to confirm that the solution obtained is indeed the Kerr spacetime. Finally, we discuss a previous suggestion in the literature for the boundary conditions for the conformal geometry on the horizon.

Abstract. Our current picture of black hole gravitational collapse relies on two assumptions: i) the resulting singularity is hidden behind an event horizon -weak cosmic censorship conjecture -and ii) spacetime eventually settles down to a stationarity state. In this setting, it follows that the minimal area containing an apparent horizon is bound by the square of the total ADM mass (Penrose inequality conjecture). Following Dain et al. 2002, we construct numerically a family of axisymmetric initial data with one or several marginally trapped surfaces. Penrose and related geometric inequalities are discused for these data. As a by-product, it is shown how Penrose inequality can be used as a diagnosis for an apparent horizon finder numerical routine.