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

Quasinormal modes of Kerr-Newman black holes: coupling of electromagnetic and gravitational perturbations

We compute numerically the quasinormal modes of Kerr-Newman black holes in the scalar case, for which the perturbation equations are separable. Then we study different approximations to decouple electromagnetic and gravitational perturbations of the Kerr-Newman metric, computing the corresponding quasinormal modes. Our results suggest that the Teukolsky-like equation derived by Dudley and Finley gives a good approximation to the dynamics of a rotating charged black hole for Q<M/2. Though insufficient to deal with Kerr-Newman based models of elementary particles, the Dudley-Finley equation should be adequate for astrophysical applications.Comment: 13 pages, 3 figures. Minor changes to match version accepted in Phys. Rev.

THE UNIQUENESS THEOREM FOR ROTATING BLACK HOLE SOLUTIONS OF SELF-GRAVITATING HARMONIC MAPPINGS

We consider rotating black hole configurations of self-gravitating maps from spacetime into arbitrary Riemannian manifolds. We first establish the integrability conditions for the Killing fields generating the stationary and the axisymmetric isometry (circularity theorem). Restricting ourselves to mappings with harmonic action, we subsequently prove that the only stationary and axisymmetric, asymptotically flat black hole solution with regular event horizon is the Kerr metric. Together with the uniqueness result for non-rotating configurations and the strong rigidity theorem, this establishes the uniqueness of the Kerr family amongst all stationary black hole solutions of self-gravitating harmonic mappings.Comment: 18 pages, latex, no figure

Extrema of Mass, First Law of Black Hole Mechanics and Staticity Theorem in Einstein-Maxwell-axion-dilaton Gravity

Using the ADM formulation of the Einstein-Maxwell axion-dilaton gravity we derived the formulas for the variation of mass and other asymptotic conserved quantities in the theory under consideration. Generalizing this kind of reasoning to the initial dota for the manifold with an interior boundary we got the generalized first law of black hole mechanics. We consider an asymptotically flat solution to the Einstein-Maxwell axion-dilaton gravity describing a black hole with a Killing vector field timelike at infinity, the horizon of which comprises a bifurcate Killing horizon with a bifurcate surface. Supposing that the Killing vector field is asymptotically orthogonal to the static hypersurface with boundary S and compact interior, we find that the solution is static in the exterior world, when the timelike vector field is normal to the horizon and has vanishing electric and axion- electric fields on static slices.Comment: 17 pages, Revtex, a few comments (introduction) and references adde

Do stringy corrections stabilize coloured black holes?

We consider hairy black hole solutions of Einstein-Yang-Mills-Dilaton theory, coupled to a Gauss-Bonnet curvature term, and we study their stability under small, spacetime-dependent perturbations. We demonstrate that the stringy corrections do not remove the sphaleronic instabilities of the coloured black holes with the number of unstable modes being equal to the number of nodes of the background gauge function. In the gravitational sector, and in the limit of an infinitely large horizon, the coloured black holes are also found to be unstable. Similar behaviour is exhibited by the magnetically charged black holes while the bulk of the neutral black holes are proven to be stable under small, gauge-dependent perturbations. Finally, the electrically charged black holes are found to be characterized only by the existence of a gravitational sector of perturbations. As in the case of neutral black holes, we demonstrate that for the bulk of electrically charged black holes no unstable modes arise in this sector.Comment: 17 pages, Revtex, comments and a reference added, version to appear in Physical Review

No hair for spherical black holes: charged and nonminimally coupled scalar field with self--interaction

We prove three theorems in general relativity which rule out classical scalar hair of static, spherically symmetric, possibly electrically charged black holes. We first generalize Bekenstein's no--hair theorem for a multiplet of minimally coupled real scalar fields with not necessarily quadratic action to the case of a charged black hole. We then use a conformal map of the geometry to convert the problem of a charged (or neutral) black hole with hair in the form of a neutral self--interacting scalar field nonminimally coupled to gravity to the preceding problem, thus establishing a no--hair theorem for the cases with nonminimal coupling parameter $\xi<0$ or $\xi\geq {1\over 2}$. The proof also makes use of a causality requirement on the field configuration. Finally, from the required behavior of the fields at the horizon and infinity we exclude hair of a charged black hole in the form of a charged self--interacting scalar field nonminimally coupled to gravity for any $\xi$.Comment: 30 pages, RevTeX. Sec.IV corrected, simplified and shortened. Corrections to Sec.IIA between Eqs. 2.7 and Eq.2.1. First two paragraphs of Sec. VC new. To appear Phys. Rev. D, Oct. 15, 199

Problems with Tunneling of Thin Shells from Black Holes

It is shown that $exp(-2 Im(\int p dr))$ is not invariant under canonical transformations in general. Specifically for shells tunneling out of black holes, this quantity is not invariant under canonical transformations. It can be interpreted as the transmission coefficient only in the cases in which it is invariant under canonical transformations. Although such cases include alpha decay, they do not include the tunneling of shells from black holes. The simplest extension to this formula which is invariant under canonical transformations is proposed. However it is shown that this gives half the correct temperature for black holes.Comment: 25 pages, 3 figures; v4: Made changes for publicatio

Late-time evolution of a self-interacting scalar field in the spacetime of dilaton black hole

We investigate the late-time tails of self-interacting (massive) scalar fields in the spacetime of dilaton black hole. Following the no hair theorem we examine the mechanism by which self-interacting scalar hair decay. We revealed that the intermediate asymptotic behavior of the considered field perturbations is dominated by an oscillatory inverse power-law decaying tail. The numerical simulations showed that at the very late-time massive self-interacting scalar hair decayed slower than any power law.Comment: 8 pages, 4 figures, to appear in Phys. Rev.

Uniqueness Theorem for Static Black Hole Solutions of sigma-models in Higher Dimensions

We prove the uniqueness theorem for self-gravitating non-linear sigma-models in higher dimensional spacetime. Applying the positive mass theorem we show that Schwarzschild-Tagherlini spacetime is the only maximally extended, static asymptotically flat solution with non-rotating regular event horizon with a constant mapping.Comment: 5 peges, Revtex, to be published in Class.Quantum Gra

Periodic-Orbit Theory of Universality in Quantum Chaos

We argue semiclassically, on the basis of Gutzwiller's periodic-orbit theory, that full classical chaos is paralleled by quantum energy spectra with universal spectral statistics, in agreement with random-matrix theory. For dynamics from all three Wigner-Dyson symmetry classes, we calculate the small-time spectral form factor $K(\tau)$ as power series in the time $\tau$. Each term $\tau^n$ of that series is provided by specific families of pairs of periodic orbits. The contributing pairs are classified in terms of close self-encounters in phase space. The frequency of occurrence of self-encounters is calculated by invoking ergodicity. Combinatorial rules for building pairs involve non-trivial properties of permutations. We show our series to be equivalent to perturbative implementations of the non-linear sigma models for the Wigner-Dyson ensembles of random matrices and for disordered systems; our families of orbit pairs are one-to-one with Feynman diagrams known from the sigma model.Comment: 31 pages, 17 figure