Einstein's Equations with Asymptotically Stable Constraint Propagation

We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The extended system of equations reproduces the usual dynamics on the constraint surface of general relativity, and therefore naturally includes the solutions to Einstein gravity. The main feature of this extended system is that, at least for a linearized version of it, the constraint surface is an attractor of the time evolution. This feature suggests that this system may be a useful alternative to Einstein's equations when obtaining numerical solutions to full, non-linear gravity.Comment: 23 pages, submitted to JMP, added reference for section

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

Stationary perturbations and infinitesimal rotations of static Einstein-Yang-Mills configurations with bosonic matter

Using the Kaluza-Klein structure of stationary spacetimes, a framework for analyzing stationary perturbations of static Einstein-Yang-Mills configurations with bosonic matter fields is presented. It is shown that the perturbations giving rise to non-vanishing ADM angular momentum are governed by a self-adjoint system of equations for a set of gauge invariant scalar amplitudes. The method is illustrated for SU(2) gauge fields, coupled to a Higgs doublet or a Higgs triplet. It is argued that slowly rotating black holes arise generically in self-gravitating non-Abelian gauge theories with bosonic matter, whereas, in general, soliton solutions do not have rotating counterparts.Comment: 8 pages, revtex, no figure

Instability of Einstein-Yang-Mills Solitons for Arbitrary Gauge Groups

We prove that static, spherically symmetric, asymptotically flat, regular solutions of the Einstein-Yang-Mills equations are unstable for arbitrary gauge groups. The proof involves the following main steps. First, we show that the frequency spectrum of a class of radial perturbations is determined by a coupled system of radial "Schroedinger equations". Eigenstates with negative eigenvalues correspond to exponentially growing modes. Using the variational principle for the ground state it is then proven that there always exist unstable modes (at least for "generic" solitons). This conclusion is reached without explicit knowledge of the possible equilibrium solutions.Comment: 11 pages, Latex, ZU-TH 4\9

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