Dirac Quasinormal modes of Schwarzschild black hole

The quasinormal modes (QNMs) associated with the decay of Dirac field perturbation around a Schwarzschild black hole is investigated by using continued fraction and Hill-determinant approaches. It is shown that the fundamental quasinormal frequencies become evenly spaced for large angular quantum number and the spacing is given by $\omega_{\lambda+1}- \omega_{\lambda}=0.38490-0.00000i$. The angular quantum number has the surprising effect of increasing real part of the quasinormal frequencies, but it almost does not affect imaginary part, especially for low overtones. In addition, the quasinormal frequencies also become evenly spaced for large overtone number and the spacing for imaginary part is $Im(\omega_{n+1})-Im(\omega_n)\approx -i/4M$ which is same as that of the scalar, electromagnetic, and gravitational perturbations.Comment: 14 pages, 5 figure

Late-Time Tails in Gravitational Collapse of a Self-Interacting (Massive) Scalar-Field and Decay of a Self-Interacting Scalar Hair

We study analytically the initial value problem for a self-interacting (massive) scalar-field on a Reissner-Nordstr\"om spacetime. Following the no-hair theorem we examine the dynamical physical mechanism by which the self-interacting (SI) hair decays. We show that the intermediate asymptotic behaviour of SI perturbations is dominated by an oscillatory inverse power-law decaying tail. We show that at late-times the decay of a SI hair is slower than any power-law. We confirm our analytical results by numerical simulations.Comment: 16 pages, 3 ps figures, Revte

On the Maximum Mass of Differentially Rotating Neutron Stars

We construct relativistic equilibrium models of differentially rotating neutron stars and show that they can support significantly more mass than their nonrotating or uniformly rotating counterparts. We dynamically evolve such ``hypermassive'' models in full general relativity and show that there do exist configurations which are dynamically stable against radial collapse and bar formation. Our results suggest that the remnant of binary neutron star coalescence may be temporarily stabilized by differential rotation, leading to delayed collapse and a delayed gravitational wave burst.Comment: 4 pages, 2 figures, uses emulateapj.sty; to appear in ApJ Letter

A detailed study of quasinormal frequencies of the Kerr black hole

We compute the quasinormal frequencies of the Kerr black hole using a continued fraction method. The continued fraction method first proposed by Leaver is still the only known method stable and accurate for the numerical determination of the Kerr quasinormal frequencies. We numerically obtain not only the slowly but also the rapidly damped quasinormal frequencies and analyze the peculiar behavior of these frequencies at the Kerr limit. We also calculate the algebraically special frequency first identified by Chandrasekhar and confirm that it coincide with the $n=8$ quasinormal frequency only at the Schwarzschild limit.Comment: REVTEX, 15 pages, 7 eps figure

Operation of EMEP ‘supersites’ in the United Kingdom. Annual report for 2008.

As part of its commitment to the UN-ECE Convention on Long-range Transboundary Air Pollution the United Kingdom operates two ‘supersites’ reporting data to the Co-operative Programme for Monitoring and Evaluation of the Long-range Transmission of Air Pollutants in Europe (EMEP). This report provides the annual summary for 2008, the second full calendar year of operation of the first EMEP ‘supersite’ to be established in the United Kingdom. Detailed operational reports have been submitted to Defra every 3 months, with unratified data. This annual report contains a summary of the ratified data for 2008. The EMEP ‘supersite’ is located in central southern Scotland at Auchencorth (3.2oW, 55.8oN), a remote rural moorland site ~20 km south-west of Edinburgh. Monitoring operations started formally on 1 June 2006. In addition to measurements made specifically under this contract, the Centre for Ecology & Hydrology also acts as local site operator for measurements made under other UK monitoring networks: the Automated Urban and Rural Network (AURN), the UK Eutrophication and Acidification Network (UKEAP), the UK Hydrocarbons Network, and the UK Heavy Metals Rural Network. Some measurements were also made under the auspices of the ‘Air Pollution Deposition Processes’ contract. All these associated networks are funded by Defra. This report summarises the measurements made between January and December 2008, and presents summary statistics on average concentrations. The site is dominated by winds from the south-west, but wind direction data highlight potential sources of airborne pollutants (power stations, conurbations). The average diurnal patterns of gases and particles are consistent with those expected for a remote rural site. The frequency distributions are presented for data where there was good data capture throughout the whole period. Some components (e.g. black carbon) show log-normal frequency distributions, while other components (e.g. ozone) have more nearly normal frequency distributions. A case study is presented for a period in June 2008, showing the influence of regional air pollutants at this remote rural site. All the data reported under the contract are shown graphically in the Appendix

Neutrino quasinormal modes of the Reissner-Nordstr\"om black hole

The neutrino quasinormal modes of the Reissner-Nordstr\"om (RN) black hole are investigated using continued fraction approach. We find, for large angular quantum number, that the quasinormal frequencies become evenly spaced and the spacing of the real part depends on the charge of the black hole and that of the imaginary part is zero. We then find that the quasinormal frequencies in the complex $\omega$ plane move counterclockwise as the charge increases. They get a spiral-like shape, moving out of their Schwarzschild value and ``looping in" towards some limiting frequency as the charge tends to the extremal value. The number of the spirals increases as the overtone number increases but it decreases as the angular quantum number increases. We also find that both the real and imaginary parts are oscillatory functions of the charge, and the oscillation becomes faster as the overtone number increases but it becomes slower as the angular quantum number increases.Comment: 11 pages, 3 figure

An Effective Search Method for Gravitational Ringing of Black Holes

We develop a search method for gravitational ringing of black holes. The gravitational ringing is due to complex frequency modes called the quasi-normal modes that are excited when a black hole geometry is perturbed. The detection of it will be a direct confirmation of the existence of a black hole. Assuming that the ringdown waves are dominated by the fundamental mode with least imaginary part, we consider matched filtering and develop an optimal method to search for the ringdown waves that have damped sinusoidal wave forms. When we use the matched filtering method, the data analysis with a lot of templates required. Here we have to ensure a proper match between the filter as a template and the real wave. It is necessary to keep the detection efficiency as high as possible under limited computational costs. First, we consider the white noise case for which the matched filtering can be studied analytically. We construct an efficient method for tiling the template space. Then, using a fitting curve of the TAMA300 DT6 noise spectrum, we numerically consider the case of colored noise. We find our tiling method developed for the white noise case is still valid even if the noise is colored.Comment: 17 pages, 9 figures. Accepted to Phys. Rev. D, Note correction to Eq. (3-25), A few comments added and minor typos correcte

On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA

Newly formed black holes are expected to emit characteristic radiation in the form of quasi-normal modes, called ringdown waves, with discrete frequencies. LISA should be able to detect the ringdown waves emitted by oscillating supermassive black holes throughout the observable Universe. We develop a multi-mode formalism, applicable to any interferometric detectors, for detecting ringdown signals, for estimating black hole parameters from those signals, and for testing the no-hair theorem of general relativity. Focusing on LISA, we use current models of its sensitivity to compute the expected signal-to-noise ratio for ringdown events, the relative parameter estimation accuracy, and the resolvability of different modes. We also discuss the extent to which uncertainties on physical parameters, such as the black hole spin and the energy emitted in each mode, will affect our ability to do black hole spectroscopy.Comment: 44 pages, 21 figures, 10 tables. Minor changes to match version in press in Phys. Rev.

Asymptotic power-law tails of massive scalar fields in Reissner-Nordstr\"{o}m background

We investigate dominant late-time tail behaviors of massive scalar fields in nearly extreme Reissner-Nordstr\"{o}m background. It is shown that the oscillatory tail of the scalar fields has the decay rate of $t^{-5/6}$ at asymptotically late times. The physical mechanism by which the asymptotic $t^{-5/6}$ tail yields and the relation between the field mass and the time scale when the tail begins to dominate, are discussed in terms of resonance backscattering due to spacetime curvature.Comment: 18 pages, 1 figure, accepted for publication in Physical Review

A note on the resonant frequencies of rapidly rotating black holes

I discuss the range of validity of Detweiler's formula for the resonant frequencies of rapidly rotating Kerr black holes. While his formula is correct for extremal black holes, it has also been commonly accepted that it describes very well the resonant frequencies of near extremal black holes, and that therefore there is a large number of modes clustering on the real axis as the black hole becomes extremal. I will show that this last statement is not only incorrect, but that it also does not follow from Detweiler's formula, provided it is handled with due care. It turns out that only the first n << -log{(r_+-r_-)/r_+} modes are well described by that formula, which translates, for any astrophysical black hole, into one or two modes only. All existing numerical data gives further support to this claim. I also discuss some implications of this result for recent investigations on the late-time dynamics of rapidly rotating black holes.Comment: 5 pages, ReVTeX