Integral equations PS-3 and moduli of pants

More than a hundred years ago H.Poincare and V.A.Steklov considered a problem for the Laplace equation with spectral parameter in the boundary conditions. Today similar problems for two adjacent domains with the spectral parameter in the conditions on the common boundary of the domains arises in a variety of situations: in justification and optimization of domain decomposition method, simple 2D models of oil extraction, (thermo)conductivity of composite materials. Singular 1D integral Poincare-Steklov equation with spectral parameter naturally emerges after reducing this 2D problem to the common boundary of the domains. We present a constructive representation for the eigenvalues and eigenfunctions of this integral equation in terms of moduli of explicitly constructed pants, one of the simplest Riemann surfaces with boundary. Essentially the solution of integral equation is reduced to the solution of three transcendent equations with three unknown numbers, moduli of pants. The discreet spectrum of the equation is related to certain surgery procedure ('grafting') invented by B.Maskit (1969), D.Hejhal (1975) and D.Sullivan- W.Thurston (1983).Comment: 27 pages, 13 figure

Measuring Black Hole Spin using X-ray Reflection Spectroscopy

I review the current status of X-ray reflection (a.k.a. broad iron line) based black hole spin measurements. This is a powerful technique that allows us to measure robust black hole spins across the mass range, from the stellar-mass black holes in X-ray binaries to the supermassive black holes in active galactic nuclei. After describing the basic assumptions of this approach, I lay out the detailed methodology focusing on "best practices" that have been found necessary to obtain robust results. Reflecting my own biases, this review is slanted towards a discussion of supermassive black hole (SMBH) spin in active galactic nuclei (AGN). Pulling together all of the available XMM-Newton and Suzaku results from the literature that satisfy objective quality control criteria, it is clear that a large fraction of SMBHs are rapidly-spinning, although there are tentative hints of a more slowly spinning population at high (M>5*10^7Msun) and low (M<2*10^6Msun) mass. I also engage in a brief review of the spins of stellar-mass black holes in X-ray binaries. In general, reflection-based and continuum-fitting based spin measures are in agreement, although there remain two objects (GROJ1655-40 and 4U1543-475) for which that is not true. I end this review by discussing the exciting frontier of relativistic reverberation, particularly the discovery of broad iron line reverberation in XMM-Newton data for the Seyfert galaxies NGC4151, NGC7314 and MCG-5-23-16. As well as confirming the basic paradigm of relativistic disk reflection, this detection of reverberation demonstrates that future large-area X-ray observatories such as LOFT will make tremendous progress in studies of strong gravity using relativistic reverberation in AGN.Comment: 19 pages. To appear in proceedings of the ISSI-Bern workshop on "The Physics of Accretion onto Black Holes" (8-12 Oct 2012). Revised version adds a missing source to Table 1 and Fig.6 (IRAS13224-3809) and corrects the referencing of the discovery of soft lags in 1H0707-495 (which were in fact first reported in Fabian et al. 2009

An overview of jets and outflows in stellar mass black holes

In this book chapter, we will briefly review the current empirical understanding of the relation between accretion state and and outflows in accreting stellar mass black holes. The focus will be on the empirical connections between X-ray states and relativistic (`radio') jets, although we are now also able to draw accretion disc winds into the picture in a systematic way. We will furthermore consider the latest attempts to measure/order jet power, and to compare it to other (potentially) measurable quantities, most importantly black hole spin.Comment: Accepted for publication in Space Science Reviews. Also to appear in the Space Sciences Series of ISSI - The Physics of Accretion on to Black Holes (Springer Publisher

Higher dimensional dust collapse with a cosmological constant

The general solution of the Einstein equation for higher dimensional (HD) spherically symmetric collapse of inhomogeneous dust in presence of a cosmological term, i.e., exact interior solutions of the Einstein field equations is presented for the HD Tolman-Bondi metrics imbedded in a de Sitter background. The solution is then matched to exterior HD Scwarschild-de Sitter. A brief discussion on the causal structure singularities and horizons is provided. It turns out that the collapse proceed in the same way as in the Minkowski background, i.e., the strong curvature naked singularities form and that the higher dimensions seem to favor black holes rather than naked singularities.Comment: 7 Pages, no figure

Radiating black hole solutions in arbitrary dimensions

We prove a theorem that characterizes a large family of non-static solutions to Einstein equations in $N$-dimensional space-time, representing, in general, spherically symmetric Type II fluid. It is shown that the best known Vaidya-based (radiating) black hole solutions to Einstein equations, in both four dimensions (4D) and higher dimensions (HD), are particular cases from this family. The spherically symmetric static black hole solutions for Type I fluid can also be retrieved. A brief discussion on the energy conditions, singularities and horizons is provided.Comment: RevTeX 9 pages, no figure

Towards a population of HMXB/NS microquasars as counterparts of low-latitude unidentified EGRET sources

The discovery of the microquasar LS 5039 well within the 95% conficence contour of the Unidentified EGRET Source (UES) 3EG J1824-1514 was a major step towards the possible association between microquasars (MQs) and UESs. The recent discovery of precessing relativistic radio jets in LS I +61 303, a source associated for long time with 2CG 135+01 and with the UES 3EG J0241+6103, has given further support to this idea. Finally, the very recently proposed association between the microquasar candidate AX J1639.0-4642 and the UES 3EG J1639-4702 points towards a population of High Mass X-ray Binary (HMXB)/Neutron Star (NS) microquasars as counterparts of low-latitude unidentified EGRET sources.Comment: 12 pages, 7 figures. Proceedings of the Conference "The Multiwavelength Approach to Unidentified Gamma-ray Sources", to appear in the journal Astrophysics and Space Scienc

Accretion and ejection in black-hole X-ray transients

Aims: We summarize the current observational picture of the outbursts of black-hole X-ray transients (BHTs), based on the evolution traced in a hardness-luminosity diagram (HLD), and we offer a physical interpretation. Methods: The basic ingredient in our interpretation is the Poynting-Robertson Cosmic Battery (PRCB, Contopoulos & Kazanas 1998), which provides locally the poloidal magnetic field needed for the ejection of the jet. In addition, we make two assumptions, easily justifiable. The first is that the mass-accretion rate to the black hole in a BHT outburst has a generic bell-shaped form. This is guaranteed by the observational fact that all BHTs start their outburst and end it at the quiescent state. The second assumption is that at low accretion rates the accretion flow is geometrically thick, ADAF-like, while at high accretion rates it is geometrically thin. Results: Both, at the beginning and the end of an outburst, the PRCB establishes a strong poloidal magnetic field in the ADAF-like part of the accretion flow, and this explains naturally why a jet is always present in the right part of the HLD. In the left part of the HLD, the accretion flow is in the form of a thin disk, and such a disk cannot sustain a strong poloidal magnetic filed. Thus, no jet is expected in this part of the HLD. The counterclockwise traversal of the HLD is explained as follows: the poloidal magnetic field in the ADAF forces the flow to remain ADAF and the source to move upwards in the HLD rather than to turn left. Thus, the history of the system determines the counterclockwise traversal of the HLD. As a result, no BHT is expected to ever traverse the entire HLD curve in the clockwise direction. Conclusions: We offer a physical interpretation of accretion and ejection in BHTs with only one parameter, the mass transfer rate.Comment: Accepted for publication in A&

Aerosolized Amiloride for the Treatment of Lung Disease in Cystic Fibrosis

To the Editor: The April 26 issue of the Journal presented encouraging results by Knowles et al. regarding the beneficial effects of aerosolized amiloride in the treatment of cystic fibrosis.1 The introduction and discussion sections of this article described the function of amiloride as an inhibitor of sodium transport in the airway epithelium, and the authors suggested that the beneficial effects observed were exerted “at least in part by increasing the clearance of secretions.” Although the results of this investigation were promising in terms of the improvement in the decline of forced vital capacity in patients with cystic fibrosis, this

Theoretical overview on high-energy emission in microquasars

Microquasar (MQ) jets are sites of particle acceleration and synchrotron emission. Such synchrotron radiation has been detected coming from jet regions of different spatial scales, which for the instruments at work nowadays appear as compact radio cores, slightly resolved radio jets, or (very) extended structures. Because of the presence of relativistic particles and dense photon, magnetic and matter fields, these outflows are also the best candidates to generate the very high-energy (VHE) gamma-rays detected coming from two of these objects, LS 5039 and LS I +61 303, and may be contributing significantly to the X-rays emitted from the MQ core. In addition, beside electromagnetic radiation, jets at different scales are producing some amount of leptonic and hadronic cosmic rays (CR), and evidences of neutrino production in these objects may be eventually found. In this work, we review on the different physical processes that may be at work in or related to MQ jets. The jet regions capable to produce significant amounts of emission at different wavelengths have been reduced to the jet base, the jet at scales of the order of the size of the system orbital semi-major axis, the jet middle scales (the resolved radio jets), and the jet termination point. The surroundings of the jet could be sites of multiwavelegnth emission as well, deserving also an insight. We focus on those scenarios, either hadronic or leptonic, in which it seems more plausible to generate both photons from radio to VHE and high-energy neutrinos. We briefly comment as well on the relevance of MQ as possible contributors to the galactic CR in the GeV-PeV range.Comment: Astrophysics & Space Science, in press (invited talk in the conference: The multimessenger approach to the high-energy gamma-ray sources", Barcelona/Catalonia, in July 4-7); 10 pages, 6 figures, 2 tables (one reference corrected