Instability Proof for Einstein-Yang-Mills Solitons and Black Holes with Arbitrary Gauge Groups

We prove that static, spherically symmetric, asymptotically flat soliton and black hole solutions of the Einstein-Yang-Mills equations are unstable for arbitrary gauge groups, at least for the ``generic" case. This conclusion is derived without explicit knowledge of the possible equilibrium solutions.Comment: 26 pages, LATEX, no figure

Cosmological Analogues of the Bartnik--McKinnon Solutions

We present a numerical classification of the spherically symmetric, static solutions to the Einstein--Yang--Mills equations with cosmological constant $\Lambda$. We find three qualitatively different classes of configurations, where the solutions in each class are characterized by the value of $\Lambda$ and the number of nodes, $n$, of the Yang--Mills amplitude. For sufficiently small, positive values of the cosmological constant, \Lambda < \Llow(n), the solutions generalize the Bartnik--McKinnon solitons, which are now surrounded by a cosmological horizon and approach the deSitter geometry in the asymptotic region. For a discrete set of values $\Lambda_{\rm reg}(n) > \Lambda_{\rm crit}(n)$, the solutions are topologically $3$--spheres, the ground state $(n=1)$ being the Einstein Universe. In the intermediate region, that is for \Llow(n) < \Lambda < \Lhig(n), there exists a discrete family of global solutions with horizon and ``finite size''.Comment: 16 pages, LaTeX, 9 Postscript figures, uses epsf.st

The generalization of the Regge-Wheeler equation for self-gravitating matter fields

It is shown that the dynamical evolution of perturbations on a static spacetime is governed by a standard pulsation equation for the extrinsic curvature tensor. The centerpiece of the pulsation equation is a wave operator whose spatial part is manifestly self-adjoint. In contrast to metric formulations, the curvature-based approach to gravitational perturbation theory generalizes in a natural way to self-gravitating matter fields. For a certain relevant subspace of perturbations the pulsation operator is symmetric with respect to a positive inner product and therefore allows spectral theory to be applied. In particular, this is the case for odd-parity perturbations of spherically symmetric background configurations. As an example, the pulsation equations for self-gravitating, non-Abelian gauge fields are explicitly shown to be symmetric in the gravitational, the Yang Mills, and the off-diagonal sector.Comment: 4 pages, revtex, no figure

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

Controlled lasing from active optomechanical resonators

Planar microcavities with distributed Bragg reflectors (DBRs) host, besides confined optical modes, also mechanical resonances due to stop bands in the phonon dispersion relation of the DBRs. These resonances have frequencies in the sub-terahertz (10E10-10E11 Hz) range with quality factors exceeding 1000. The interaction of photons and phonons in such optomechanical systems can be drastically enhanced, opening a new route toward manipulation of light. Here we implemented active semiconducting layers into the microcavity to obtain a vertical-cavity surface-emitting laser (VCSEL). Thereby three resonant excitations -photons, phonons, and electrons- can interact strongly with each other providing control of the VCSEL laser emission: a picosecond strain pulse injected into the VCSEL excites long-living mechanical resonances therein. As a result, modulation of the lasing intensity at frequencies up to 40 GHz is observed. From these findings prospective applications such as THz laser control and stimulated phonon emission may emerge

Observation of the transition from lasing driven by a bosonic to a fermionic reservoir in a GaAs quantum well microcavity

We show that by monitoring the free carrier reservoir in a GaAs-based quantum well microcavity under non-resonant pulsed optical pumping, lasing supported by a fermionic reservoir (photon lasing) can be distinguished from lasing supported by a reservoir of bosons (polariton lasing). Carrier densities are probed by measuring the photocurrent between lateral contacts deposited directly on the quantum wells of a microcavity that are partially exposed by wet chemical etching. We identify two clear thresholds in the input-output characteristic of the photoluminescence signal which can be attributed to polariton and photon lasing, respectively. The power dependence of the probed photocurrent shows a distinct kink at the threshold power for photon lasing due to increased radiative recombination of free carriers as stimulated emission into the cavity mode sets in. At the polariton lasing threshold on the other hand, the nonlinear increase of the luminescence is caused by stimulated scattering of exciton-polaritons to the ground state which do not contribute directly to the photocurrent.PostprintPeer reviewe

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

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