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

Recovering S1S^1-invariant metrics on S2S^2 from the equivariant spectrum

We prove an inverse spectral result for $S^1$-invariant metrics on $S^2$ based on the so-called asymptotic equivariant spectrum. This is roughly the spectrum together with large weights of the $S^1$ action on the eigenspaces. Our result generalizes an inverse spectral result of the first and last named authors, together with Victor Guillemin, concerning $S^1$-invariant metrics on $S^2$ which are invariant under the antipodal map. We use higher order terms in the asymptotic expansion of a natural spectral measure associated with the Laplacian and the $S^1$ action.Comment: 16 pages; minor revisions throughout following comments from referee

Astrophysical signatures of boson stars: quasinormal modes and inspiral resonances

Compact bosonic field configurations, or boson stars, are promising dark matter candidates which have been invoked as an alternative description for the supermassive compact objects in active galactic nuclei. Boson stars can be comparable in size and mass to supermassive black holes and they are hard to distinguish by electromagnetic observations. However, boson stars do not possess an event horizon and their global spacetime structure is different from that of a black hole. This leaves a characteristic imprint in the gravitational-wave emission, which can be used as a discriminant between black holes and other horizonless compact objects. Here we perform a detailed study of boson stars and their gravitational-wave signatures in a fully relativistic setting, a study which was lacking in the existing literature in many respects. We construct several fully relativistic boson star configurations, and we analyze their geodesic structure and free oscillation spectra, or quasinormal modes. We explore the gravitational and scalar response of boson star spacetimes to an inspiralling stellar-mass object and compare it to its black hole counterpart. We find that a generic signature of compact boson stars is the resonant-mode excitation by a small compact object on stable quasi-circular geodesic motion.Comment: 20 pages, 8 figures. v2: minor corrections, version to be published in Phys. Rev. D. v3: final versio

Slowly Rotating Anisotropic Neutron Stars in General Relativity and Scalar-Tensor Theory

Some models (such as the Skyrme model, a low-energy effective field theory for QCD) suggest that the high-density matter prevailing in neutron star interiors may be significantly anisotropic. Anisotropy is known to affect the bulk properties of nonrotating neutron stars in General Relativity. In this paper we study the effects of anisotropy on slowly rotating stars in General Relativity. We also consider one of the most popular extensions of Einstein's theory, namely scalar-tensor theories allowing for spontaneous scalarization (a phase transition similar to spontaneous magnetization in ferromagnetic materials). Anisotropy affects the moment of inertia of neutron stars (a quantity that could potentially be measured in binary pulsar systems) in both theories. We find that the effects of scalarization increase (decrease) when the tangential pressure is bigger (smaller) than the radial pressure, and we present a simple criterion to determine the onset of scalarization by linearizing the scalar-field equation. Our calculations suggest that binary pulsar observations may constrain the degree of anisotropy or even, more optimistically, provide evidence for anisotropy in neutron star cores.Comment: 19 pages, 7 figures, 1 table. Matches version in press in CQG. Fixed small typo