Massive vector fields on the Schwarzschild spacetime: quasinormal modes and bound states

We study the propagation of a massive vector or Proca field on the Schwarzschild spacetime. The field equations are reduced to a one-dimensional wave equation for the odd-parity part of the field and two coupled equations for the even-parity part of the field. We use numerical techniques based on solving (scalar or matrix-valued) three-term recurrence relations to compute the spectra of both quasi-normal modes and quasi-bound states, which have no massless analogue, complemented in the latter case by a forward-integration method. We study the radial equations analytically in both the near-horizon and far-field regions and use a matching procedure to compute the associated spectra in the small-mass limit. Finally, we comment on extending our results to the Kerr geometry and its phenomenological relevance for hidden photons arising e.g. in string theory compactifications.Comment: 15 pages, 8 figures; minor corrections, to be published in Phys. Rev.

Bound states of spin-half particles in a static gravitational field close to the black hole field

We consider the bound-state energy levels of a spin-1/2 fermion in the gravitational field of a near-black hole object. In the limit that the metric of the body becomes singular, all binding energies tend to the rest-mass energy (i.e. total energy approaches zero). We present calculations of the ground state energy for three specific interior metrics (Florides, Soffel and Schwarzschild) for which the spectrum collapses and becomes quasi-continuous in the singular metric limit. The lack of zero or negative energy states prior to this limit being reached prevents particle pair production occurring. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides and Soffel metrics the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the centre. The behaviour of the energy level spectrum is discussed in the context of the semi-classical approximation and using general properties of the metric.Comment: 16 pages, 6 Figures. Submitted to General Relativity and Gravitatio

Resonance and absorption spectra of the Schwarzschild black hole for massive scalar perturbations: a complex angular momentum analysis

We reexamine some aspects of scattering by a Schwarzschild black hole in the framework of complex angular momentum techniques. More precisely, we consider, for massive scalar perturbations, the high-energy behavior of the resonance spectrum and of the absorption cross section by emphasizing analytically the role of the mass. This is achieved (i) by deriving asymptotic expansions for the Regge poles of the $S$-matrix and then for the associated weakly damped quasinormal frequencies and (ii) by taking into account the analytic structure of the greybody factors which allows us to extract by resummation the physical information encoded in the absorption cross section.Comment: v2: Minor changes to match the published version. v3: Typos correcte

Warm-Start AlphaZero Self-Play Search Enhancements

Recently, AlphaZero has achieved landmark results in deep reinforcement learning, by providing a single self-play architecture that learned three different games at super human level. AlphaZero is a large and complicated system with many parameters, and success requires much compute power and fine-tuning. Reproducing results in other games is a challenge, and many researchers are looking for ways to improve results while reducing computational demands. AlphaZero's design is purely based on self-play and makes no use of labeled expert data ordomain specific enhancements; it is designed to learn from scratch. We propose a novel approach to deal with this cold-start problem by employing simple search enhancements at the beginning phase of self-play training, namely Rollout, Rapid Action Value Estimate (RAVE) and dynamically weighted combinations of these with the neural network, and Rolling Horizon Evolutionary Algorithms (RHEA). Our experiments indicate that most of these enhancements improve the performance of their baseline player in three different (small) board games, with especially RAVE based variants playing strongly

Global maps of the magnetic thickness and magnetization of the Earth’s lithosphere

International audienceWe have constructed global maps of the large-scale magnetic thickness and magnetization of Earth's lithosphere. Deriving such large-scale maps based on lithospheric magnetic field measurements faces the challenge of the masking effect of the core field. In this study, the maps were obtained through analyses in the spectral domain by means of a new regional spatial power spectrum based on the Revised Spherical Cap Harmonic Analysis (R-SCHA) formalism. A series of regional spectral analyses were conducted covering the entire Earth. The R-SCHA surface power spectrum for each region was estimated using the NGDC-720 spherical harmonic (SH) model of the lithospheric magnetic field, which is based on satellite, aeromagnetic, and marine measurements. These observational regional spectra were fitted to a recently proposed statistical expression of the power spectrum of Earth's lithospheric magnetic field, whose free parameters include the thickness and magnetization of the magnetic sources. The resulting global magnetic thickness map is compared to other crustal and magnetic thickness maps based upon different geophysical data. We conclude that the large-scale magnetic thickness of the lithosphere is on average confined to a layer that does not exceed the Moho

Stock markets and effective exchange rates in European countries: threshold cointegration findings

© 2015, Eurasia Business and Economics Society. The nexus between stock markets and exchange rates is examined in the case of eight European countries. The sample consists of four economies with national currencies and four that have adopted the euro. Thus, if differences between the two groups in the relationship governing the two markets exist, they will be unveiled. To this effect, a threshold cointegration methodology is adopted that allows for more reliable inferences to be drawn for both the short and long run nexus between the two markets. Monthly data is used covering the period 01/2000–12/2014. The findings reported herein offer support in favor of the portfolio approach thesis over the recent economic crisis period, but this finding is not the case for the entire sample. Bidirectional causality is found for Norway and the UK, pointing to a currency effect on stock markets. In view of the findings reported herein, policies aiming at reducing uncertainty in the stock markets can exert beneficial effects on currency markets

Continental crust beneath southeast Iceland

The magmatic activity (0–16 Ma) in Iceland is linked to a deep mantle plume that has been active for the past 62 My. Icelandic and northeast Atlantic basalts contain variable proportions of two enriched components, interpreted as recycled oceanic crust supplied by the plume, and subcontinental lithospheric mantle derived from the nearby continental margins. A restricted area in southeast Iceland—and especially the Öræfajökull volcano—is characterized by a unique enriched-mantle component (EM2-like) with elevated 87Sr/86Sr and 207Pb/204Pb. Here, we demonstrate through modeling of Sr–Nd–Pb abundances and isotope ratios that the primitive Öræfajökull melts could have assimilated 2–6% of underlying continental crust before differentiating to more evolved melts. From inversion of gravity anomaly data (crustal thickness), analysis of regional magnetic data, and plate reconstructions, we propose that continental crust beneath southeast Iceland is part of ∼350-km-long and 70-km-wide extension of the Jan Mayen Microcontinent (JMM). The extended JMM was marginal to East Greenland but detached in the Early Eocene (between 52 and 47 Mya); by the Oligocene (27 Mya), all parts of the JMM permanently became part of the Eurasian plate following a westward ridge jump in the direction of the Iceland plume