Quasi-Normal Modes of Stars and Black Holes

Perturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present the theory of quasi-normal modes of compact objects from both the mathematical and astrophysical points of view. The discussion includes perturbations of black holes (Schwarzschild, Reissner-Nordstr\"om, Kerr and Kerr-Newman) and relativistic stars (non-rotating and slowly-rotating). The properties of the various families of quasi-normal modes are described, and numerical techniques for calculating quasi-normal modes reviewed. The successes, as well as the limits, of perturbation theory are presented, and its role in the emerging era of numerical relativity and supercomputers is discussed.Comment: 74 pages, 7 figures, Review article for "Living Reviews in Relativity

Semi-analytic results for quasi-normal frequencies

The last decade has seen considerable interest in the quasi-normal frequencies [QNFs] of black holes (and even wormholes), both asymptotically flat and with cosmological horizons. There is wide agreement that the QNFs are often of the form omega_n = (offset) + i n (gap), though some authors have encountered situations where this behaviour seems to fail. To get a better understanding of the general situation we consider a semi-analytic model based on a piecewise Eckart (Poeschl-Teller) potential, allowing for different heights and different rates of exponential falloff in the two asymptotic directions. This model is sufficiently general to capture and display key features of the black hole QNFs while simultaneously being analytically tractable, at least for asymptotically large imaginary parts of the QNFs. We shall derive an appropriate "quantization condition" for the asymptotic QNFs, and extract as much analytic information as possible. In particular, we shall explicitly verify that the (offset)+ i n (gap) behaviour is common but not universal, with this behaviour failing unless the ratio of rates of exponential falloff on the two sides of the potential is a rational number. (This is "common but not universal" in the sense that the rational numbers are dense in the reals.) We argue that this behaviour is likely to persist for black holes with cosmological horizons.Comment: V1: 28 pages, no figures. V2: 3 references added, no physics changes. V3: 29 pages, 9 references added, no physics changes; V4: reformatted, now 27 pages. Some clarifications, comparison with results obtained by monodromy techniques. This version accepted for publication in JHEP. V5: Minor typos fixed. Compatible with published versio

Gravitational waves from single neutron stars: an advanced detector era survey

With the doors beginning to swing open on the new gravitational wave astronomy, this review provides an up-to-date survey of the most important physical mechanisms that could lead to emission of potentially detectable gravitational radiation from isolated and accreting neutron stars. In particular we discuss the gravitational wave-driven instability and asteroseismology formalism of the f- and r-modes, the different ways that a neutron star could form and sustain a non-axisymmetric quadrupolar "mountain" deformation, the excitation of oscillations during magnetar flares and the possible gravitational wave signature of pulsar glitches. We focus on progress made in the recent years in each topic, make a fresh assessment of the gravitational wave detectability of each mechanism and, finally, highlight key problems and desiderata for future work.Comment: 39 pages, 12 figures, 2 tables. Chapter of the book "Physics and Astrophysics of Neutron Stars", NewCompStar COST Action 1304. Minor corrections to match published versio

Distributions of charged massive scalars and fermions from evaporating higher-dimensional black holes

A detailed numerical analysis is performed to obtain the Hawking spectrum for charged, massive brane scalars and fermions on the approximate background of a brane charged rotating higher-dimensional black hole constructed in arXiv:0907.5107. We formulate the problem in terms of a "spinor-like" first order system of differential wave equations not only for fermions, but for scalars as well and integrate it numerically. Flux spectra are presented for non-zero mass, charge and rotation, confirming and extending previous results based on analytic approximations. In particular we describe an inverted charge splitting at low energies, which is not present in four or five dimensions and increases with the number of extra dimensions. This provides another signature of the evaporation of higher-dimensional black holes in TeV scale gravity scenarios.Comment: 19 pages, 6 figures, minor typos corrected, 1 page added with a discussion on higher spins, added reference

Superconducting spintronics

The interaction between superconducting and spin-polarized orders has recently emerged as a major research field following a series of fundamental breakthroughs in charge transport in superconductor-ferromagnet heterodevices which promise new device functionality. Traditional studies which combine spintronics and superconductivity have mainly focused on the injection of spin-polarized quasiparticles into superconducting materials. However, a complete synergy between superconducting and magnetic orders turns out to be possible through the creation of spin-triplet Cooper pairs which are generated at carefully engineered superconductor interfaces with ferromagnetic materials. Currently, there is intense activity focused on identifying materials combinations which merge superconductivity and spintronics in order to enhance device functionality and performance. The results look promising: it has been shown, for example, that superconducting order can greatly enhance central effects in spintronics such as spin injection and magnetoresistance. Here, we review the experimental and theoretical advances in this field and provide an outlook for upcoming challenges related to the new concept of superconducting spintronics.J.L. was supported by the Research Council of Norway, Grants No. 205591 and 216700. J.W.A.R. was supported by the UK Royal Society and the Leverhulme Trust through an International Network Grant (IN-2013-033).This is the accepted manuscript. The final version is available at http://www.nature.com/nphys/journal/v11/n4/full/nphys3242.html

N-Terminal Arginines Modulate Plasma-Membrane Localization of Kv7.1/KCNE1 Channel Complexes

BACKGROUND AND OBJECTIVE: The slow delayed rectifier current (I(Ks)) is important for cardiac action potential termination. The underlying channel is composed of Kv7.1 α-subunits and KCNE1 β-subunits. While most evidence suggests a role of KCNE1 transmembrane domain and C-terminus for the interaction, the N-terminal KCNE1 polymorphism 38G is associated with reduced I(Ks) and atrial fibrillation (a human arrhythmia). Structure-function relationship of the KCNE1 N-terminus for I(Ks) modulation is poorly understood and was subject of this study. METHODS: We studied N-terminal KCNE1 constructs disrupting structurally important positively charged amino-acids (arginines) at positions 32, 33, 36 as well as KCNE1 constructs that modify position 38 including an N-terminal truncation mutation. Experimental procedures included molecular cloning, patch-clamp recording, protein biochemistry, real-time-PCR and confocal microscopy. RESULTS: All KCNE1 constructs physically interacted with Kv7.1. I(Ks) resulting from co-expression of Kv7.1 with non-atrial fibrillation '38S' was greater than with any other construct. Ionic currents resulting from co-transfection of a KCNE1 mutant with arginine substitutions ('38G-3xA') were comparable to currents evoked from cells transfected with an N-terminally truncated KCNE1-construct ('Δ1-38'). Western-blots from plasma-membrane preparations and confocal images consistently showed a greater amount of Kv7.1 protein at the plasma-membrane in cells co-transfected with the non-atrial fibrillation KCNE1-38S than with any other construct. CONCLUSIONS: The results of our study indicate that N-terminal arginines in positions 32, 33, 36 of KCNE1 are important for reconstitution of I(Ks). Furthermore, our results hint towards a role of these N-terminal amino-acids in membrane representation of the delayed rectifier channel complex

Differential Association between HERG and KCNE1 or KCNE2

The small proteins encoded by KCNE1 and KCNE2 have both been proposed as accessory subunits for the HERG channel. Here we report our investigation into the cell biology of the KCNE-HERG interaction. In a co-expression system, KCNE1 was more readily co-precipitated with co-expressed HERG than was KCNE2. When forward protein trafficking was prevented (either by Brefeldin A or engineering an ER-retention/retrieval signal onto KCNE cDNA) the intracellular abundance of KCNE2 and its association with HERG markedly increased relative to KCNE1. HERG co-localized more completely with KCNE1 than with KCNE2 in all the membrane-processing compartments of the cell (ER, Golgi and plasma membrane). By surface labeling and confocal immunofluorescence, KCNE2 appeared more abundant at the cell surface compared to KCNE1, which exhibited greater co-localization with the ER-marker calnexin. Examination of the extracellular culture media showed that a significant amount of KCNE2 was extracellular (both soluble and membrane-vesicle-associated). Taken together, these results suggest that during biogenesis of channels HERG is more likely to assemble with KCNE1 than KCNE2 due to distinctly different trafficking rates and retention in the cell rather than differences in relative affinity. The final channel subunit constitution, in vivo, is likely to be determined by a combination of relative cell-to-cell expression rates and differential protein processing and trafficking

Rotating Stars in Relativity

Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information one could obtain about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on the equilibrium properties and on the nonaxisymmetric instabilities in f-modes and r-modes have been updated and several new sections have been added on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity.Comment: 101 pages, 18 figures. The full online-readable version of this article, including several animations, will be published in Living Reviews in Relativity at http://www.livingreviews.org