Perturbation theory for self-gravitating gauge fields I: The odd-parity sector

A gauge and coordinate invariant perturbation theory for self-gravitating non-Abelian gauge fields is developed and used to analyze local uniqueness and linear stability properties of non-Abelian equilibrium configurations. It is shown that all admissible stationary odd-parity excitations of the static and spherically symmetric Einstein-Yang-Mills soliton and black hole solutions have total angular momentum number $\ell = 1$, and are characterized by non-vanishing asymptotic flux integrals. Local uniqueness results with respect to non-Abelian perturbations are also established for the Schwarzschild and the Reissner-Nordstr\"om solutions, which, in addition, are shown to be linearly stable under dynamical Einstein-Yang-Mills perturbations. Finally, unstable modes with $\ell = 1$ are also excluded for the static and spherically symmetric non-Abelian solitons and black holes.Comment: 23 pages, revtex, no figure

On rotational excitations and axial deformations of BPS monopoles and Julia-Zee dyons

It is shown that Julia-Zee dyons do not admit slowly rotating excitations. This is achieved by investigating the complete set of stationary excitations which can give rise to non-vanishing angular momentum. The relevant zero modes are parametrized in a gauge invariant way and analyzed by means of a harmonic decomposition. Since general arguments show that the solutions to the linearized Bogomol'nyi equations cannot contribute to the angular momentum, the relevant modes are governed by a set of electric and a set of non self-dual magnetic perturbation equations. The absence of axial dipole deformations is also established.Comment: 22 pages, Revtex, no figure

Global behavior of solutions to the static spherically symmetric EYM equations

The set of all possible spherically symmetric magnetic static Einstein-Yang-Mills field equations for an arbitrary compact semi-simple gauge group $G$ was classified in two previous papers. Local analytic solutions near the center and a black hole horizon as well as those that are analytic and bounded near infinity were shown to exist. Some globally bounded solutions are also known to exist because they can be obtained by embedding solutions for the $G=SU(2)$ case which is well understood. Here we derive some asymptotic properties of an arbitrary global solution, namely one that exists locally near a radial value $r_{0}$, has positive mass $m(r)$ at $r_{0}$ and develops no horizon for all $r>r_{0}$. The set of asymptotic values of the Yang-Mills potential (in a suitable well defined gauge) is shown to be finite in the so-called regular case, but may form a more complicated real variety for models obtained from irregular rotation group actions.Comment: 43 page

Pulsation of Spherically Symmetric Systems in General Relativity

The pulsation equations for spherically symmetric black hole and soliton solutions are brought into a standard form. The formulae apply to a large class of field theoretical matter models and can easily be worked out for specific examples. The close relation to the energy principle in terms of the second variation of the Schwarzschild mass is also established. The use of the general expressions is illustrated for the Einstein-Yang-Mills and the Einstein-Skyrme system.Comment: 21 pages, latex, no figure

Stable monopole and dyon solutions in the Einstein-Yang-Mills theory in asymptotically anti-de Sitter Space

A continuum of new monopole and dyon solutions in the Einstein-Yang-Mills theory in asymptotically anti-de Sitter space are found. They are regular everywhere and specified with their mass, and non-Abelian electric and magnetic charges. A class of monopole solutions which have no node in non-Abelian magnetic fields are shown to be stable against spherically symmetric linear perturbations.Comment: 9 pages with 5 figures. Revised version. To appear in Phys Rev Let

Monopoles, Dyons and Black Holes in the Four-Dimensional Einstein-Yang-Mills Theory

A continuum of monopole, dyon and black hole solutions exist in the Einstein-Yang-Mills theory in asymptotically anti-de Sitter space. Their structure is studied in detail. The solutions are classified by non-Abelian electric and magnetic charges and the ADM mass. The stability of the solutions which have no node in non-Abelian magnetic fields is established. There exist critical spacetime solutions which terminate at a finite radius, and have universal behavior. The moduli space of the solutions exhibits a fractal structure as the cosmological constant approaches zero.Comment: 36 Pages, 16 Figures. Minor typos corrected and one figure modifie

Physical interpretation of gauge invariant perturbations of spherically symmetric space-times

By calculating the Newman-Penrose Weyl tensor components of a perturbed spherically symmetric space-time with respect to invariantly defined classes of null tetrads, we give a physical interpretation, in terms of gravitational radiation, of odd parity gauge invariant metric perturbations. We point out how these gauge invariants may be used in setting boundary and/or initial conditions in perturbation theory.Comment: 6 pages. To appear in PR

Correlation of Pool Boiling Curves for the Homologous Group: Freons

Nomenclature C L = specific heat of liquid g = gravitational acceleration h fg = latent heat of evaporation k L = thermal conductivity of liquid P c = thermodynamic critical pressure <7> <7max> tfmin = heat flux, maximum flux, minimum flux Introduction A knowledge of the complete boiling curve q versus AT for a liquid, including the regimes of nucleate boiling, transition boiling, and film boiling, and the peak and minimum crisis points is needed for the design and operation of various types of heat transfer equipment. No general method exists for predicting the complete curve. Most difficult is the prediction of the nucleate boiling curve, the transition curve, and the temperature that separates the two. If the curve for every liquid at every pressure must be determined experimentally, we are faced with a formidable task. This paper shows that some simplification is possible for members of a homologous group

Electroencephalographic source imaging: a prospective study of 152 operated epileptic patients

Electroencephalography is mandatory to determine the epilepsy syndrome. However, for the precise localization of the irritative zone in patients with focal epilepsy, costly and sometimes cumbersome imaging techniques are used. Recent small studies using electric source imaging suggest that electroencephalography itself could be used to localize the focus. However, a large prospective validation study is missing. This study presents a cohort of 152 operated patients where electric source imaging was applied as part of the pre-surgical work-up allowing a comparison with the results from other methods. Patients (n = 152) with >1 year postoperative follow-up were studied prospectively. The sensitivity and specificity of each imaging method was defined by comparing the localization of the source maximum with the resected zone and surgical outcome. Electric source imaging had a sensitivity of 84% and a specificity of 88% if the electroencephalogram was recorded with a large number of electrodes (128–256 channels) and the individual magnetic resonance image was used as head model. These values compared favourably with those of structural magnetic resonance imaging (76% sensitivity, 53% specificity), positron emission tomography (69% sensitivity, 44% specificity) and ictal/interictal single-photon emission-computed tomography (58% sensitivity, 47% specificity). The sensitivity and specificity of electric source imaging decreased to 57% and 59%, respectively, with low number of electrodes (<32 channels) and a template head model. This study demonstrated the validity and clinical utility of electric source imaging in a large prospective study. Given the low cost and high flexibility of electroencephalographic systems even with high channel counts, we conclude that electric source imaging is a highly valuable tool in pre-surgical epilepsy evaluation