39 research outputs found
Critical bubbles and implications for critical black strings
We demonstrate the existence of gravitational critical phenomena in higher
dimensional electrovac bubble spacetimes. To this end, we study linear
fluctuations about families of static, homogeneous spherically symmetric bubble
spacetimes in Kaluza-Klein theories coupled to a Maxwell field. We prove that
these solutions are linearly unstable and posses a unique unstable mode with a
growth rate that is universal in the sense that it is independent of the family
considered. Furthermore, by a double analytical continuation this mode can be
seen to correspond to marginally stable stationary modes of perturbed black
strings whose periods are integer multiples of the Gregory-Laflamme critical
length. This allow us to rederive recent results about the behavior of the
critical mass for large dimensions and to generalize them to the charged black
string case.Comment: A reference to unpublished work for the case q=2, by J. Hovdebo adde
Schwarzschild black holes can wear scalar wigs
We study the evolution of a massive scalar field surrounding a Schwarzschild
black hole and find configurations that can survive for arbitrarily long times,
provided the black hole or the scalar field mass is small enough. In
particular, both ultra-light scalar field dark matter around supermassive black
holes and axion-like scalar fields around primordial black holes can survive
for cosmological times. Moreover, these results are quite generic, in the sense
that fairly arbitrary initial data evolves, at late times, as a combination of
those long-lived configurations.Comment: 5 pages, 3 figures. Accepted for publication in Physical Review
Letter
Physical interpretation of gauge invariant perturbations of spherically symmetric space-times
By calculating the Newman-Penrose Weyl tensor components of a perturbed
spherically symmetric space-time with respect to invariantly defined classes of
null tetrads, we give a physical interpretation, in terms of gravitational
radiation, of odd parity gauge invariant metric perturbations. We point out how
these gauge invariants may be used in setting boundary and/or initial
conditions in perturbation theory.Comment: 6 pages. To appear in PR
Stability properties of black holes in self-gravitating nonlinear electrodynamics
We analyze the dynamical stability of black hole solutions in
self-gravitating nonlinear electrodynamics with respect to arbitrary linear
fluctuations of the metric and the electromagnetic field. In particular, we
derive simple conditions on the electromagnetic Lagrangian which imply linear
stability in the domain of outer communication. We show that these conditions
hold for several of the regular black hole solutions found by Ayon-Beato and
Garcia.Comment: 15 pages, no figure
Instability of wormholes supported by a ghost scalar field. I. Linear stability analysis
We examine the linear stability of static, spherically symmetric wormhole
solutions of Einstein's field equations coupled to a massless ghost scalar
field. These solutions are parametrized by the areal radius of their throat and
the product of the masses at their asymptotically flat ends. We prove that all
these solutions are unstable with respect to linear fluctuations and possess
precisely one unstable, exponentially in time growing mode. The associated time
scale is shown to be of the order of the wormhole throat divided by the speed
of light. The nonlinear evolution is analyzed in a subsequent article.Comment: 12 pages, 1 figure, minor changes, to appear in Classical and Quantum
Gravit
Instability of wormholes supported by a ghost scalar field. II. Nonlinear evolution
We analyze the nonlinear evolution of spherically symmetric wormhole
solutions coupled to a massless ghost scalar field using numerical methods. In
a previous article we have shown that static wormholes with these properties
are unstable with respect to linear perturbations. Here we show that depending
on the initial perturbation the wormholes either expand or decay to a
Schwarzschild black hole. We estimate the time scale of the expanding solutions
and the ones collapsing to a black hole and show that they are consistent in
the regime of small perturbations with those predicted from perturbation
theory. In the collapsing case, we also present a systematic study of the final
black hole horizon and discuss the possibility for a luminous signal to travel
from one universe to the other and back before the black hole forms. In the
expanding case, the wormholes seem to undergo an exponential expansion, at
least during the run time of our simulations.Comment: 16 pages, 15 figures, minor modifications, to appear in Classical and
Quantum Gravit
On the existence of dyons and dyonic black holes in Einstein-Yang-Mills theory
We study dyonic soliton and black hole solutions of the
Einstein-Yang-Mills equations in asymptotically anti-de Sitter space. We prove
the existence of non-trivial dyonic soliton and black hole solutions in a
neighbourhood of the trivial solution. For these solutions the magnetic gauge
field function has no zeros and we conjecture that at least some of these
non-trivial solutions will be stable. The global existence proof uses local
existence results and a non-linear perturbation argument based on the (Banach
space) implicit function theorem.Comment: 23 pages, 2 figures. Minor revisions; references adde
On the Use of Multipole Expansion in Time Evolution of Non-linear Dynamical Systems and Some Surprises Related to Superradiance
A new numerical method is introduced to study the problem of time evolution
of generic non-linear dynamical systems in four-dimensional spacetimes. It is
assumed that the time level surfaces are foliated by a one-parameter family of
codimension two compact surfaces with no boundary and which are conformal to a
Riemannian manifold C. The method is based on the use of a multipole expansion
determined uniquely by the induced metric structure on C. The approach is fully
spectral in the angular directions. The dynamics in the complementary 1+1
Lorentzian spacetime is followed by making use of a fourth order finite
differencing scheme with adaptive mesh refinement.
In checking the reliability of the introduced new method the evolution of a
massless scalar field on a fixed Kerr spacetime is investigated. In particular,
the angular distribution of the evolving field in to be superradiant scattering
is studied. The primary aim was to check the validity of some of the recent
arguments claiming that the Penrose process, or its field theoretical
correspondence---superradiance---does play crucial role in jet formation in
black hole spacetimes while matter accretes onto the central object. Our
findings appear to be on contrary to these claims as the angular dependence of
a to be superradiant scattering of a massless scalar field does not show any
preference of the axis of rotation. In addition, the process of superradiance,
in case of a massless scalar field, was also investigated. On contrary to the
general expectations no energy extraction from black hole was found even though
the incident wave packets was fine tuned to be maximally superradiant. Instead
of energy extraction the to be superradiant part of the incident wave packet
fails to reach the ergoregion rather it suffers a total reflection which
appears to be a new phenomenon.Comment: 49 pages, 11 figure
Covariant Perturbations of Schwarzschild Black Holes
We present a new covariant and gauge-invariant perturbation formalism for
dealing with spacetimes having spherical symmetry (or some preferred spatial
direction) in the background, and apply it to the case of gravitational wave
propagation in a Schwarzschild black hole spacetime. The 1+3 covariant approach
is extended to a `1+1+2 covariant sheet' formalism by introducing a radial unit
vector in addition to the timelike congruence, and decomposing all covariant
quantities with respect to this. The background Schwarzschild solution is
discussed and a covariant characterisation is given. We give the full
first-order system of linearised 1+1+2 covariant equations, and we show how, by
introducing (time and spherical) harmonic functions, these may be reduced to a
system of first-order ordinary differential equations and algebraic constraints
for the 1+1+2 variables which may be solved straightforwardly. We show how both
the odd and even parity perturbations may be unified by the discovery of a
covariant, frame- and gauge-invariant, transverse-traceless tensor describing
gravitational waves, which satisfies a covariant wave equation equivalent to
the Regge-Wheeler equation for both even and odd parity perturbations. We show
how the Zerilli equation may be derived from this tensor, and derive a similar
transverse traceless tensor equivalent to this equation. The so-called
`special' quasinormal modes with purely imaginary frequency emerge naturally.
The significance of the degrees of freedom in the choice of the two frame
vectors is discussed, and we demonstrate that, for a certain frame choice, the
underlying dynamics is governed purely by the Regge-Wheeler tensor. The two
transverse-traceless Weyl tensors which carry the curvature of gravitational
waves are discussed.Comment: 23 pages, 1 figure, Revtex 4. Submitted to Classical and Quantum
Gravity. Revised version is significantly streamlined with an important error
corrected which simplifies the presentatio
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 , 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 are also excluded for the static and spherically
symmetric non-Abelian solitons and black holes.Comment: 23 pages, revtex, no figure