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

A no-go on strictly stationary spacetimes in four/higher dimensions

We show that strictly stationary spacetimes cannot have non-trivial configurations of form fields/complex scalar fields and then the spacetime should be exactly Minkowski or anti-deSitter spacetimes depending on the presence of negative cosmological constant. That is, self-gravitating complex scalar fields and form fields cannot exist.Comment: 8 page

First clear evidence of quantum chaos in the bound states of an atomic nucleus

We study the spectral fluctuations of the $^{208}$Pb nucleus using the complete experimental spectrum of 151 states up to excitation energies of $6.20$ MeV recently identified at the Maier-Leibnitz-Laboratorium at Garching, Germany. For natural parity states the results are very close to the predictions of Random Matrix Theory (RMT) for the nearest-neighbor spacing distribution. A quantitative estimate of the agreement is given by the Brody parameter $\omega$, which takes the value $\omega=0$ for regular systems and $\omega \simeq 1$ for chaotic systems. We obtain $\omega=0.85 \pm 0.02$ which is, to our knowledge, the closest value to chaos ever observed in experimental bound states of nuclei. By contrast, the results for unnatural parity states are far from RMT behavior. We interpret these results as a consequence of the strength of the residual interaction in $^{208}$Pb, which, according to experimental data, is much stronger for natural than for unnatural parity states. In addition our results show that chaotic and non-chaotic nuclear states coexist in the same energy region of the spectrum.Comment: 9 pages, 1 figur

Dressing a black hole with non-minimally coupled scalar field hair

We investigate the possibility of dressing a four-dimensional black hole with classical scalar field hair which is non-minimally coupled to the space-time curvature. Our model includes a cosmological constant but no self-interaction potential for the scalar field. We are able to rule out black hole hair except when the cosmological constant is negative and the constant governing the coupling to the Ricci scalar curvature is positive. In this case, non-trivial hairy black hole solutions exist, at least some of which are linearly stable. However, when the coupling constant becomes too large, the black hole hair becomes unstable.Comment: 17 pages, 7 figures, uses iopart.cls. Minor changes, accepted for publication in Classical and Quantum Gravit

A Mass Bound for Spherically Symmetric Black Hole Spacetimes

Requiring that the matter fields are subject to the dominant energy condition, we establish the lower bound $(4\pi)^{-1} \kappa {\cal A}$ for the total mass $M$ of a static, spherically symmetric black hole spacetime. (${\cal A}$ and $\kappa$ denote the area and the surface gravity of the horizon, respectively.) Together with the fact that the Komar integral provides a simple relation between $M - (4\pi)^{-1} \kappa A$ and the strong energy condition, this enables us to prove that the Schwarzschild metric represents the only static, spherically symmetric black hole solution of a selfgravitating matter model satisfying the dominant, but violating the strong energy condition for the timelike Killing field $K$ at every point, that is, $R(K,K) \leq 0$. Applying this result to scalar fields, we recover the fact that the only black hole configuration of the spherically symmetric Einstein-Higgs model with arbitrary non-negative potential is the Schwarzschild spacetime with constant Higgs field. In the presence of electromagnetic fields, we also derive a stronger bound for the total mass, involving the electromagnetic potentials and charges. Again, this estimate provides a simple tool to prove a ``no-hair'' theorem for matter fields violating the strong energy condition.Comment: 16 pages, LATEX, no figure

Mass of Colored Black Holes

New results pertaining to colored static black hole solutions to the Einstein-Yang-Mills equations are obtained. The isolated horizons framework is used to define the concept of Hamiltonian Horizon Mass of the black hole. An unexpected relation between the ADM and Horizon masses of the black hole solution with the ADM mass of the corresponding Bartnik-McKinnon soliton is found. These results can be generalized to other non-linear theories and they suggest a general testing bed for the instability of the corresponding hairy black holes.Comment: 8 pages, no figures, Revtex file. Minor changes made to clarify some formulas. References updated. Final version to appear in PRD/15

On Black Hole Scalar Hair in Asymptotically Anti de Sitter Spacetimes

The unexpected discovery of hairy black hole solutions in theories with scalar fields simply by considering asymptotically Anti de-Sitter, rather than asymptotically flat, boundary conditions is analyzed in a way that exhibits in a clear manner the differences between the two situations. It is shown that the trivial Schwarzschild Anti de Sitter becomes unstable in some of these situations, and the possible relevance of this fact for the ADS/CFT conjecture is pointed out.Comment: 12 pages. Published versio

Vacuum solutions of five dimensional Einstein equations generated by inverse scattering method

We study stationary and axially symmetric two solitonic solutions of five dimensional vacuum Einstein equations by using the inverse scattering method developed by Belinski and Zakharov. In this generation of the solutions, we use five dimensional Minkowski spacetime as a seed. It is shown that if we restrict ourselves to the case of one angular momentum component, the generated solution coincides with a black ring solution with a rotating two sphere which was found by Mishima and Iguchi recently.Comment: 10 pages, accepted for publication in Physical Review

Higher-dimensional solitons and black holes with a non-minimally coupled scalar field

We study higher-dimensional soliton and hairy black hole solutions of the Einstein equations non-minimally coupled to a scalar field. The scalar field has no self-interaction potential but a cosmological constant is included. Non-trivial solutions exist only when the cosmological constant is negative and the constant governing the coupling of the scalar field to the Ricci scalar curvature is positive. At least some of these solutions are stable when this coupling constant is not too large.Comment: 17 pages, revtex4, 21 figures, minor changes to match published versio