1,913 research outputs found

    Unstable fields in Kerr spacetimes

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    We show that both the interior region r<MM2a2r<M-\sqrt{M^2-a^2} of a Kerr black hole and the a2>M2a^2>M^2 Kerr naked singularity admit unstable solutions of the Teukolsky equation for any value of the spin weight. For every harmonic number there is at least one axially symmetric mode that grows exponentially in time and decays properly in the radial directions. These can be used as Debye potentials to generate solutions for the scalar, Weyl spinor, Maxwell and linearized gravity field equations on these backgrounds, satisfying appropriate spatial boundary conditions and growing exponentially in time, as shown in detail for the Maxwell case. It is suggested that the existence of the unstable modes is related to the so called "time machine" region, where the axial Killing vector field is time-like, and the Teukolsky equation, restricted to axially symmetric fields, changes its character from hyperbolic to elliptic

    The initial value problem for linearized gravitational perturbations of the Schwarzschild naked singularity

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    The coupled equations for the scalar modes of the linearized Einstein equations around Schwarzschild's spacetime were reduced by Zerilli to a 1+1 wave equation with a potential VV, on a field Ψz\Psi_z. For smooth metric perturbations Ψz\Psi_z is singular at rs=6M/(1)(+2)r_s=-6M/(\ell-1)(\ell+2), \ell the mode harmonic number, and VV has a second order pole at rsr_s. This is irrelevant to the black hole exterior stability problem, where r>2M>0r>2M>0, and rs<0r_s <0, but it introduces a non trivial problem in the naked singular case where M0M0, and the singularity appears in the relevant range of rr. We solve this problem by developing a new approach to the evolution of the even mode, based on a {\em new gauge invariant function}, Ψ^\hat \Psi -related to Ψz\Psi_z by an intertwiner operator- that is a regular function of the metric perturbation {\em for any value of MM}. This allows to address the issue of evolution of gravitational perturbations in this non globally hyperbolic background, and to complete the proof of the linear instability of the Schwarzschild naked singularity, by showing that a previously found unstable mode is excitable by generic initial data. This is further illustrated by numerically solving the linearized equations for suitably chosen initial data.Comment: typos corrected, references adde

    The economic crisis and changes in work-family arrangements in six European countries

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    Over the past decades, there has been a substantial increase in female labour force participation, and the number of dual-earner and female-earner households has risen throughout western countries. However, the recent economic crisis has caused large losses in employment for both women and men, potentially yielding unexpected consequences for the evolution of work\u2013family arrangements. This article carries out a comparative analysis of the relationship between the 2008/2009 economic crisis and work\u2013family arrangements in Europe. Using data for six countries from the European Union Statistics on Income and Living Conditions, this article fills a gap in the literature by addressing three issues: (1) whether work\u2013family arrangements have changed from before to after the beginning of the economic downturn in countries with different gender and welfare regimes (Germany, Greece, Spain, France, Sweden and the United Kingdom), (2) whether changes in work\u2013family arrangements have occurred at different levels of the social strata and (3) whether couples have moved from dual-earner to male- or female-breadwinner. The results indicate changes in work\u2013family arrangements in those countries worst hit by the economic crisis, Greece and Spain, where dual-earner and male-breadwinner households have decreased and no-earner and femalemain- earner households have increased. Moreover, the results show that in these two countries, all social strata \u2013 proxied through women\u2019s level of education \u2013 have been affected by the crisis. In contrast, only moderate changes in work\u2013family arrangements among all women can be observed in countries less hit by the economic downturn. The findings for the two southern European countries are troubling, as the increases in no-earner and female-breadwinner households point to worsening economic conditions throughout the population and to a halt in the process that for several decades had been leading to more equality in the distribution of employment between gender

    Vacuum solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory

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    The classification of certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is presented. The spacelike section of the class of metrics under consideration is a warped product of the real line with a nontrivial base manifold. For arbitrary values of the Gauss-Bonnet coupling, the base manifold must be Einstein with an additional scalar restriction. The geometry of the boundary can be relaxed only when the Gauss-Bonnet coupling is related with the cosmological and Newton constants, so that the theory admits a unique maximally symmetric solution. This additional freedom in the boundary metric allows the existence of three main branches of geometries in the bulk, containing new black holes and wormholes in vacuum.Comment: Prepared for the proceedings of the 7th Alexander Friedmann International Seminar on Gravitation and Cosmology, July 2008, Joao Pessoa, Brasil. 4 pages, References adde

    The Best Is Yet to Come? Attitudes towards gender roles among adolescents in 36 countries

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    In the present article, we look at attitudes toward gender roles among young women and men in 36 countries with different levels of societal gender inequality. By applying multilevel models to data from the International Civic and Citizenship Education Study 2009, the study contributes to our understanding of gender inequality by showing that (a) both young women and young men (in 8th grade; Mage = 14.39 years) display more gender-egalitarian attitudes in countries with higher levels of societal gender equality; (b) young women in all countries have more egalitarian attitudes toward gender roles than young men do, but (c) the gender gap in attitudes is more evident in more egalitarian contexts; and (d) a higher level of maternal education is associated with more gender-egalitarian attitudes among young women. In contrast, no statistically significant association emerges between maternal employment and young men\u2019s attitudes. Overall, the findings suggest that adolescents in different contexts are influenced by the dominant societal discourse on gender inequality, which they interiorize and display through their own attitudes toward gender roles. However, the findings also indicate that young women are more responsive to external cues than young men are. This result, coupled with the fact that young men in egalitarian contexts have not adopted gender-egalitarian attitudes to the same extent as young women, is concerning because it suggests a slowdown in the achievement of societal gender equality that is still far from being reache

    Hyperk\"ahler torsion structures invariant by nilpotent Lie groups

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    We study HKT structures on nilpotent Lie groups and on associated nilmanifolds. We exhibit three weak HKT structures on R8\R^8 which are homogeneous with respect to extensions of Heisenberg type Lie groups. The corresponding hypercomplex structures are of a special kind, called abelian. We prove that on any 2-step nilpotent Lie group all invariant HKT structures arise from abelian hypercomplex structures. Furthermore, we use a correspondence between abelian hypercomplex structures and subspaces of sp(n){\frak sp}(n) to produce continuous families of compact and noncompact of manifolds carrying non isometric HKT structures. Finally, geometrical properties of invariant HKT structures on 2-step nilpotent Lie groups are obtained.Comment: LateX, 12 page