Nature of singularities in gravitational collapse

We discuss several aspects of cosmic censorship hypothesis. There is evidence both in favor and against the hypothesis. On one hand one can prove that cosmic censorship holds in several special cases and on the other hand there is a number of special solutions of Einstein equations in which it is violated. One way to resolve cosmic censorship problem is to test it observationally. We point out to several possibilities of such tests using present and future instruments.Comment: 11 pages, PTPTeX, references added, typos corrected, submitted to Proceedings of the Yukawa-Kyoto International Seminar 9

On the differentiability of Cauchy horizons

Chrusciel and Galloway constructed a Cauchy horizon that is nondifferentiable on a dense set. We prove that in a certain class of Cauchy horizons densely nondifferentiable Cauchy horizons are generic. We show that our class of densely nondifferentiable Cauchy horizons implies the existence of densely nondifferentiable Cauchy horizons arising from partial Cauchy surfaces and also the existence of densely nondifferentiable black hole event horizons.Comment: 9 pages, LaTe

The White Dwarf -- White Dwarf galactic background in the LISA data

LISA (Laser Interferometer Space Antenna) is a proposed space mission, which will use coherent laser beams exchanged between three remote spacecraft to detect and study low-frequency cosmic gravitational radiation. In the low-part of its frequency band, the LISA strain sensitivity will be dominated by the incoherent superposition of hundreds of millions of gravitational wave signals radiated by inspiraling white-dwarf binaries present in our own galaxy. In order to estimate the magnitude of the LISA response to this background, we have simulated a synthesized population that recently appeared in the literature. We find the amplitude of the galactic white-dwarf binary background in the LISA data to be modulated in time, reaching a minimum equal to about twice that of the LISA noise for a period of about two months around the time when the Sun-LISA direction is roughly oriented towards the Autumn equinox. Since the galactic white-dwarfs background will be observed by LISA not as a stationary but rather as a cyclostationary random process with a period of one year, we summarize the theory of cyclostationary random processes, present the corresponding generalized spectral method needed to characterize such process, and make a comparison between our analytic results and those obtained by applying our method to the simulated data. We find that, by measuring the generalized spectral components of the white-dwarf background, LISA will be able to infer properties of the distribution of the white-dwarfs binary systems present in our Galaxy.Comment: 36 pages, 15 figure

On the stability of a superspinar

The superspinar proposed by Gimon and Horava is a rapidly rotating compact entity whose exterior is described by the over-spinning Kerr geometry. The compact entity itself is expected to be governed by superstringy effects, and in astrophysical scenarios it can give rise to interesting observable phenomena. Earlier it was suggested that the superspinar may not be stable but we point out here that this does not necessarily follow from earlier studies. We show, by analytically treating the Teukolsky equations by Detwiler's method, that in fact there are infinitely many boundary conditions that make the superspinar stable, and that the modes will decay in time. It follows that we need to know more on the physical nature of the superspinar in order to decide on its stability in physical reality.Comment: 5 page

TCF7L2 mediates the cellular and behavioral response to chronic lithium treatment in animal models

AbstractThe mechanism of lithium's therapeutic action remains obscure, hindering the discovery of safer treatments for bipolar disorder. Lithium can act as an inhibitor of the kinase GSK3α/β, which in turn negatively regulates β-catenin, a co-activator of LEF1/TCF transcription factors. However, unclear is whether therapeutic levels of lithium activate β-catenin in the brain, and whether this activation could have a therapeutic significance. To address this issue we chronically treated mice with lithium. Although the level of non-phospho-β-catenin increased in all of the brain areas examined, β-catenin translocated into cellular nuclei only in the thalamus. Similar results were obtained when thalamic and cortical neurons were treated with a therapeutically relevant concentration of lithium in vitro. We tested if TCF7L2, a member of LEF1/TCF family that is highly expressed in the thalamus, facilitated the activation of β-catenin. Silencing of Tcf7l2 in thalamic neurons prevented β-catenin from entering the nucleus, even when the cells were treated with lithium. Conversely, when Tcf7l2 was ectopically expressed in cortical neurons, β-catenin shifted to the nucleus, and lithium augmented this process. Lastly, we silenced tcf7l2 in zebrafish and exposed them to lithium for 3 days, to evaluate whether TCF7L2 is involved in the behavioral response. Lithium decreased the dark-induced activity of control zebrafish, whereas the activity of zebrafish with tcf7l2 knockdown was unaltered. We conclude that therapeutic levels of lithium activate β-catenin selectively in thalamic neurons. This effect is determined by the presence of TCF7L2, and potentially contributes to the therapeutic response

Simulation of the White Dwarf -- White Dwarf galactic background in the LISA data

LISA (Laser Interferometer Space Antenna) is a proposed space mission, which will use coherent laser beams exchanged between three remote spacecraft to detect and study low-frequency cosmic gravitational radiation. In the low-part of its frequency band, the LISA strain sensitivity will be dominated by the incoherent superposition of hundreds of millions of gravitational wave signals radiated by inspiraling white-dwarf binaries present in our own galaxy. In order to estimate the magnitude of the LISA response to this background, we have simulated a synthesized population that recently appeared in the literature. We find the amplitude of the galactic white-dwarf binary background in the LISA data to be modulated in time, reaching a minimum equal to about twice that of the LISA noise for a period of about two months around the time when the Sun-LISA direction is roughly oriented towards the Autumn equinox. Since the galactic white-dwarfs background will be observed by LISA not as a stationary but rather as a cyclostationary random process with a period of one year, we summarize the theory of cyclostationary random processes and present the corresponding generalized spectral method needed to characterize such process. We find that, by measuring the generalized spectral components of the white-dwarf background, LISA will be able to infer properties of the distribution of the white-dwarfs binary systems present in our Galaxy.Comment: 14 pages and 6 figures. Submitted to Classical and Quantum Gravity (Proceedings of GWDAW9