Towards a cross-correlation approach to strong-field dynamics in Black Hole spacetimes

The qualitative and quantitative understanding of near-horizon gravitational dynamics in the strong-field regime represents a challenge both at a fundamental level and in astrophysical applications. Recent advances in numerical relativity and in the geometric characterization of black hole horizons open new conceptual and technical avenues into the problem. We discuss here a research methodology in which spacetime dynamics is probed through the cross-correlation of geometric quantities constructed on the black hole horizon and on null infinity. These two hypersurfaces respond to evolving gravitational fields in the bulk, providing canonical "test screens" in a "scattering"-like perspective onto spacetime dynamics. More specifically, we adopt a 3+1 Initial Value Problem approach to the construction of generic spacetimes and discuss the role and properties of dynamical trapping horizons as canonical inner "screens" in this context. We apply these ideas and techniques to the study of the recoil dynamics in post-merger binary black holes, an important issue in supermassive galactic black hole mergers.Comment: 16 pages, 5 figures, contribution to the proceedings volume of the Spanish Relativity Meeting ERE2011: "Towards new paradigms", Madrid, Spain, 29 Aug-2 Sep 201

Dielectric properties of Li2O-3B2O3 glasses

The frequency and temperature dependence of the dielectric constant and the electrical conductivity of the transparent glasses in the composition Li2O-3B2O3 (LBO) were investigated in the 100 Hz- 10 MHz frequency range. The dielectric constant and the loss in the low frequency regime were electrode material dependent. Dielectric and electrical relaxations were respectively analyzed using the Cole-Cole and electric modulus formalisms. The dielectric relaxation mechanism was discussed in the framework of electrode and charge carrier (hopping of the ions) related polarization using generalized Cole-Cole expression. The frequency dependent electrical conductivity was rationalized using Jonscher's power law. The activation energy associated with the dc conductivity was 0.80 \pm 0.02 eV, which was ascribed to the motion of Li+ ions in the glass matrix. The activation energy associated with dielectric relaxation was almost equal to that of the dc conductivity, indicating that the same species took part in both the processes. Temperature dependent behavior of the frequency exponent (n) suggested that the correlated barrier hopping model was the most apposite to rationalize the electrical transport phenomenon in Li2O-3B2O3 glasses. These glasses on heating at 933 K/10h resulted in the known non-linear optical phase LiB3O5.Comment: 32 pages, 13 figure

Charge and momentum transfer in supercooled melts: Why should their relaxation times differ?

The steady state values of the viscosity and the intrinsic ionic-conductivity of quenched melts are computed, in terms of independently measurable quantities. The frequency dependence of the ac dielectric response is estimated. The discrepancy between the corresponding characteristic relaxation times is only apparent; it does not imply distinct mechanisms, but stems from the intrinsic barrier distribution for $\alpha$-relaxation in supercooled fluids and glasses. This type of intrinsic ``decoupling'' is argued not to exceed four orders in magnitude, for known glassformers. We explain the origin of the discrepancy between the stretching exponent $\beta$, as extracted from $\epsilon(\omega)$ and the dielectric modulus data. The actual width of the barrier distribution always grows with lowering the temperature. The contrary is an artifact of the large contribution of the dc-conductivity component to the modulus data. The methodology allows one to single out other contributions to the conductivity, as in ``superionic'' liquids or when charge carriers are delocalized, implying that in those systems, charge transfer does not require structural reconfiguration.Comment: submitted to J Chem Phy

Gravitational wave recoil in Robinson-Trautman spacetimes

We consider the gravitational recoil due to non-reflection-symmetric gravitational wave emission in the context of axisymmetric Robinson-Trautman spacetimes. We show that regular initial data evolve generically into a final configuration corresponding to a Schwarzschild black-hole moving with constant speed. For the case of (reflection-)symmetric initial configurations, the mass of the remnant black-hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some recent numerical results that have been appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the non-linear regime of the Robinson-Trautman equations, we show that the recoil velocity can be estimated with good accuracy from some asymmetry measures (namely the first odd moments) of the initial data. The extension for the non-axisymmetric case and the implications of our results for realistic situations involving head-on collision of two black holes are also discussed.Comment: 9 pages, 6 figures, final version to appear in PR