Static Cosmological Solutions of the Einstein-Yang-Mills-Higgs Equations

Numerical evidence is presented for the existence of a new family of static, globally regular `cosmological' solutions of the spherically symmetric Einstein-Yang-Mills-Higgs equations. These solutions are characterized by two natural numbers ($m\geq 1$, $n\geq 0$), the number of nodes of the Yang-Mills and Higgs field respectively. The corresponding spacetimes are static with spatially compact sections with 3-sphere topology.Comment: 7 pages, 5 figures, LaTe

Non-Abelian black holes: The inside story

Recent progress in understanding of the internal structure of non-Abelian black holes is discussed. Talk given at the international Workshop on The Internal Structure of Black Holes and Spacetime Singularities, Haifa, Israel, June 29 -- July 3, 1997.Comment: 23 pages, latex, contains 12 eps files combined in 8 figure

Self-similar solutions of semilinear wave equations with a focusing nonlinearity

We prove that in three space dimensions a nonlinear wave equation $u_{tt}-\Delta u = u^p$ with $p\geq 7$ being an odd integer has a countable family of regular spherically symmetric self-similar solutions.Comment: 12 pages, 3 figures, minor corrections to match the published versio

Mass inflation inside non-Abelian black holes

The interior geometry of static, spherically symmetric black holes of the Einstein-Yang-Mills-Higgs theory is analyzed. It is found that in contrast to the Abelian case generically no inner (Cauchy) horizon is formed inside non-Abelian black holes. Instead the solutions come close to a Cauchy horizon but then undergo an enormous growth of the mass function, a phenomenon which can be termed `mass inflation' in analogy to what is observed for perturbations of the Reissner-Nordstr{ø}m solution. A significant difference between the theories with and without a Higgs field is observed. Without a Higgs field the YM field induces repeated cycles of mass inflation -- taking the form of violent `explosions' -- interrupted by quiescent periods and subsequent approaches to an almost Cauchy horizon. With the Higgs field no such cycles occur. Besides the generic solutions there are non-generic families with a Schwarzschild, Reissner-Nordstr{ø}m and a pseudo Reissner-Nordstr{ø}m type singularity at $r=0

Integrable Systems in Stringy Gravity

Static axisymmetric Einstein-Maxwell-Dilaton and stationary axisymmetric Einstein-Maxwell-Dilaton-Axion (EMDA) theories in four space-time dimensions are shown to be integrable by means of the inverse scattering transform method. The proof is based on the coset-space representation of the 4-dim theory in a space-time admitting a Killing vector field. Hidden symmetry group of the four-dimensional EMDA theory, unifying T and S string dualities, is shown to be Sp(2, R) acting transitively on the coset Sp(2, R)/U(2). In the case of two-parameter Abelian space-time isometry group, the hidden symmetry is the corresponding infinite-dimensional group of the Geroch-Kinnersley-Chitre type.Comment: 8 pages, LATEX, MSU-DTP-94/21, October 9

Universality of global dynamics for the cubic wave equation

We consider the initial value problem for the spherically symmetric, focusing cubic wave equation in three spatial dimensions. We give numerical and analytical evidence for the existence of a universal attractor which encompasses both global and blowup solutions. As a byproduct we get an explicit description of the critical behavior at the threshold of blowup.Comment: 13 pages, 15 figures. Uses IOP-style. Updated to conform with published versio

The effect of post-meal walking on 24-hour central blood pressure in young women with and without excess adiposity

Post-meal walking (PMW) performed after breakfast, lunch, and dinner has been demonstrated to reduce blood glucose. However, no studies have examined the potential additive benefits of post-meal walking exercise on daytime central blood pressure (BP) in young women. METHODS: Thirteen physically inactive, non-hypertensive women (Age: 20±1 years; percent body fat: 28.2±13%) completed the study during the early follicular or placebo phase of their contraceptive cycle. Participants completed a control day (CON; no exercise/excess physical activity) and PMW day (3 bouts x 15 minutes of brisk walking) over five days in random order. Daytime ambulatory BP and accelerometry data (to estimate METs) were measured and compared. RESULTS: PMW increased metabolic expenditure (PMW= 35.8±1.44 vs. CON= 33.7±0.94 METs, p0.05 for all). CONCLUSION: PMW does not lead to reductions in central BP in young, physically inactive women

Harrison transformation of hyperelliptic solutions and charged dust disks

We use a Harrison transformation on solutions to the stationary axisymmetric Einstein equations to generate solutions of the Einstein-Maxwell equations. The case of hyperelliptic solutions to the Ernst equation is studied in detail. Analytic expressions for the metric and the multipole moments are obtained. As an example we consider the transformation of a family of counter-rotating dust disks. The resulting solutions can be interpreted as disks with currents and matter with a purely azimuthal pressure or as two streams of freely moving charged particles. We discuss interesting limiting cases as the extreme limit where the charge becomes identical to the mass, and the ultrarelativistic limit where the central redshift diverges.Comment: 20 pages, 9 figure

Binary black hole spacetimes with a helical Killing vector

Binary black hole spacetimes with a helical Killing vector, which are discussed as an approximation for the early stage of a binary system, are studied in a projection formalism. In this setting the four dimensional Einstein equations are equivalent to a three dimensional gravitational theory with a $SL(2,\mathbb{C})/SO(1,1)$ sigma model as the material source. The sigma model is determined by a complex Ernst equation. 2+1 decompositions of the 3-metric are used to establish the field equations on the orbit space of the Killing vector. The two Killing horizons of spherical topology which characterize the black holes, the cylinder of light where the Killing vector changes from timelike to spacelike, and infinity are singular points of the equations. The horizon and the light cylinder are shown to be regular singularities, i.e. the metric functions can be expanded in a formal power series in the vicinity. The behavior of the metric at spatial infinity is studied in terms of formal series solutions to the linearized Einstein equations. It is shown that the spacetime is not asymptotically flat in the strong sense to have a smooth null infinity under the assumption that the metric tends asymptotically to the Minkowski metric. In this case the metric functions have an oscillatory behavior in the radial coordinate in a non-axisymmetric setting, the asymptotic multipoles are not defined. The asymptotic behavior of the Weyl tensor near infinity shows that there is no smooth null infinity.Comment: to be published in Phys. Rev. D, minor correction