302 research outputs found
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 or . 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 .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 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 as power series in the time .
Each term 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
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