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

The management of common recurrent headaches by chiropractors: A descriptive analysis of a nationally representative survey

© 2018 The Author(s). Background: Headache management is common within chiropractic clinical settings; however, little is yet known about how this provider group manage headache sufferers. The aim of this study is to report on the prevalence of headache patients found within routine chiropractic practice and to assess how chiropractors approach key aspects of headache management applicable to primary care settings. Methods: A 31-item cross-sectional survey was distributed to a national sample of chiropractors (n = 1050) to report on practitioner approach to headache diagnosis, interdisciplinary collaboration, treatment and outcome assessment of headache patients who present with recurrent headache disorders. Results: The survey attracted a response rate of 36% (n = 381). One in five new patients present to chiropractors with a chief complaint of headache. The majority of chiropractors provide headache diagnosis for common primary (84.6%) and secondary (90.4%) headaches using formal headache classification criteria. Interdisciplinary referral for headache management was most often with CAM providers followed by GPs. Advice on headache triggers, stress management, spinal manipulation, soft tissue therapies and prescriptive neck exercises were the most common therapeutic approaches to headache management. Conclusion: Headache patients make up a substantial proportion of chiropractic caseload. The majority of chiropractors managing headache engage in headache diagnosis and interdisciplinary patient management. More research information is needed to understand the headache types and level of headache chronicity and disability common to chiropractic patient populations to further assess the healthcare needs of this patient population

Massive fields tend to form highly oscillating self-similarly expanding shells

The time evolution of self-interacting spherically symmetric scalar fields in Minkowski spacetime is investigated based on the use of Green's theorem. It is shown that a massive Klein-Gordon field can be characterized by the formation of certain expanding shell structures where all the shells are built up by very high frequency oscillations. This oscillation is found to be modulated by the product of a simple time decaying factor of the form $t^{-{3}/{2}}$ and of an essentially self-similar expansion. Apart from this self-similar expansion the developed shell structure is preserved by the evolution. In particular, the energy transported by each shell appears to be time independent.Comment: 10 pages, to appear in Phys. Rev.

The treatment of migraine patients within chiropractic: Analysis of a nationally representative survey of 1869 chiropractors

© 2017 The Author(s). Background: While the clinical role of manual therapies in migraine management is unclear, the use of chiropractors for this condition is considerable. The aim of this study is to evaluate the prevalence and characteristics of chiropractors who frequently manage patients with migraine. Methods: A national cross-sectional survey of chiropractors collected information on practitioner characteristics, clinical management characteristics and practice settings. A secondary analysis was conducted on 1869 respondents who reported on their migraine caseload to determine the predictors associated with the frequent management of patients with migraine. Results: A large proportion of chiropractors report having a high migraine caseload (HMC) (n = 990; 53.0%). The strongest factors predicting a chiropractor having a HMC include the frequent treatment of patients with axial neck pain (OR = 2.89; 95%CI: 1.18, 7.07), thoracic pain (referred/radicular) (OR = 2.52; 95%CI: 1.58, 3.21) and non-musculoskeletal disorders (OR = 3.06; 95%CI: 2.13, 4.39). Conclusions: Several practice-setting and clinical management characteristics are associated with chiropractors managing a HMC. These findings raise key questions about the therapeutic approach to chiropractic migraine management that deserves further examination. There is a need for more primary research to assess the approach to headache and migraine management provided by chiropractors and to understand the prevalence, burden and comorbidities associated with migraine found within chiropractic patient populations. This information is vital in helping to inform safe, effective and coordinated care for migraine sufferers within the wider health system

Quasinormal Modes, the Area Spectrum, and Black Hole Entropy

The results of canonical quantum gravity concerning geometric operators and black hole entropy are beset by an ambiguity labelled by the Immirzi parameter. We use a result from classical gravity concerning the quasinormal mode spectrum of a black hole to fix this parameter in a new way. As a result we arrive at the Bekenstein - Hawking expression of $A/4 l_P^2$ for the entropy of a black hole and in addition see an indication that the appropriate gauge group of quantum gravity is SO(3) and not its covering group SU(2).Comment: 4 pages, 2 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

Quasinormal Modes of Dirty Black Holes

Quasinormal mode (QNM) gravitational radiation from black holes is expected to be observed in a few years. A perturbative formula is derived for the shifts in both the real and the imaginary part of the QNM frequencies away from those of an idealized isolated black hole. The formulation provides a tool for understanding how the astrophysical environment surrounding a black hole, e.g., a massive accretion disk, affects the QNM spectrum of gravitational waves. We show, in a simple model, that the perturbed QNM spectrum can have interesting features.Comment: 4 pages. Published in PR

Quasi-normal modes of AdS black holes : A superpotential approach

A novel method, based on superpotentials is proposed for obtaining the quasi-normal modes of anti-de Sitter black holes. This is inspired by the case of the three-dimensional BTZ black hole, where the quasi-normal modes can be obtained exactly and are proportional to the surface gravity. Using this approach, the quasi-normal modes of the five dimensional Schwarzschild anti-deSitter black hole are computed numerically. The modes again seem to be proportional to the surface gravity for very small and very large black holes. They reflect the well-known instability of small black holes in anti-deSitter space.Comment: LaTeX, 17 pages, 5 eps figures, 1 eepic figure, minor typos correcte

High-Order Contamination in the Tail of Gravitational Collapse

It is well known that the late-time behaviour of gravitational collapse is {\it dominated} by an inverse power-law decaying tail. We calculate {\it higher-order corrections} to this power-law behaviour in a spherically symmetric gravitational collapse. The dominant ``contamination'' is shown to die off at late times as $M^2t^{-4}\ln(t/M)$. This decay rate is much {\it slower} than has been considered so far. It implies, for instance, that an `exact' (numerical) determination of the power index to within $\sim 1$ requires extremely long integration times of order $10^4 M$. We show that the leading order fingerprint of the black-hole electric {\it charge} is of order $Q^2t^{-4}$.Comment: 12 pages, 2 figure