101,523 research outputs found
The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit
The effect of small forced symmetry breaking on the dynamics near a structurally stable heteroclinic
cycle connecting two equilibria and a periodic orbit is investigated. This type of system is known
to exhibit complicated, possibly chaotic dynamics including irregular switching of sign of various
phase space variables, but details of the mechanisms underlying the complicated dynamics have
not previously been investigated. We identify global bifurcations that induce the onset of chaotic
dynamics and switching near a heteroclinic cycle of this type, and by construction and analysis
of approximate return maps, locate the global bifurcations in parameter space. We find there is a
threshold in the size of certain symmetry-breaking terms below which there can be no persistent
switching. Our results are illustrated by a numerical example
Black Holes in Einstein-Aether Theory
We study black hole solutions in general relativity coupled to a unit
timelike vector field dubbed the "aether". To be causally isolated a black hole
interior must trap matter fields as well as all aether and metric modes. The
theory possesses spin-0, spin-1, and spin-2 modes whose speeds depend on four
coupling coefficients. We find that the full three-parameter family of local
spherically symmetric static solutions is always regular at a metric horizon,
but only a two-parameter subset is regular at a spin-0 horizon. Asymptotic
flatness imposes another condition, leaving a one-parameter family of regular
black holes. These solutions are compared to the Schwarzschild solution using
numerical integration for a special class of coupling coefficients. They are
very close to Schwarzschild outside the horizon for a wide range of couplings,
and have a spacelike singularity inside, but differ inside quantitatively. Some
quantities constructed from the metric and aether oscillate in the interior as
the singularity is approached. The aether is at rest at spatial infinity and
flows into the black hole, but differs significantly from the the 4-velocity of
freely-falling geodesics.Comment: 22 pages, 6 figures; v2: minor editing; v3: corrected overall sign in
twist formula and an error in the equation for the aether stress tensor.
Results unchanged since correct form was used in calculations; v4: corrected
minor typ
The Caustic Ring Model of the Milky Way Halo
We present a proposal for the full phase space distribution of the Milky Way
halo. The model is axially and reflection symmetric and its time evolution is
self-similar. It describes the halo as a set of discrete dark matter flows with
stated densities and velocity vectors everywhere. We first discuss the general
conditions under which the time evolution of a cold collisionless
self-gravitating fluid is self-similar, and show that symmetry is not necessary
for self-similarity. When spherical symmetry is imposed, the model is the same
as described by Fillmore and Goldreich, and by Bertschinger, twenty-three years
ago. The spherically symmetric model depends on one dimensionless parameter
and two dimensionful parameters. We set = 0.3, a value
consistent with the slope of the power spectrum of density perturbations on
galactic scales. The dimensionful parameters are determined by the Galactic
rotation velocity (220 km/s) at the position of the Sun and by the age of the
Galaxy (13.7 Gyr). The properties of the outer caustics are derived in the
spherically symmetric model. The structure of the inner halo depends on the
angular momentum distribution of the dark matter particles. We assume that
distribution to be axial and reflection symmetric, and dominated by net overall
rotation. The inner caustics are rings whose radii are determined in terms of a
single additional parameter . We summarize the observational
evidence in support of the model. The evidence is consistent with
= 0.18 in Concordance Cosmology, equivalent to = 0.26 in
Einstein - de Sitter cosmology. We give formulas to estimate the flow densities
and velocity vectors anywhere in the Milky Way halo. The properties of the
first forty flows at the location of the Earth are listed.Comment: 35 pages, 6 figure
Yangian symmetry in deformed WZNW models on squashed spheres
We introduce a deformation of the Wess-Zumino-Novikov-Witten model with
three-dimensional squashed sphere target space. We show how with an appropriate
choice of Wess--Zumino and boundary terms it is possible to construct an
infinite family of conserved charges realizing an SU(2) Yangian. Finally we
discuss the running of the squashing parameter under renormalization group
flow.Comment: 12 pages, 1 figure, references adde
Geometric flows in Horava-Lifshitz gravity
We consider instanton solutions of Euclidean Horava-Lifshitz gravity in four
dimensions satisfying the detailed balance condition. They are described by
geometric flows in three dimensions driven by certain combinations of the
Cotton and Ricci tensors as well as the cosmological-constant term. The
deformation curvature terms can have competing behavior leading to a variety of
fixed points. The instantons interpolate between any two fixed points, which
are vacua of topologically massive gravity with Lambda > 0, and their action is
finite. Special emphasis is placed on configurations with SU(2) isometry
associated with homogeneous but generally non-isotropic Bianchi IX model
geometries. In this case, the combined Ricci-Cotton flow reduces to an
autonomous system of ordinary differential equations whose properties are
studied in detail for different couplings. The occurrence and stability of
isotropic and anisotropic fixed points are investigated analytically and some
exact solutions are obtained. The corresponding instantons are classified and
they are all globally R x S^3 and complete spaces. Generalizations to
higher-dimensional gravities are also briefly discussed.Comment: 67 pages, 16 figures; more solutions found, 1 extra figure, 1 more
reference added in v2; minor typos corrected in v3 (to appear in JHEP); an
acknowledgement added in v
On Spin Dependence of Relativistic Acoustic Geometry
This work makes the first ever attempt to understand the influence of the
black hole background space-time in determining the fundamental properties of
the embedded relativistic acoustic geometry. To accomplish such task, the role
of the spin angular momentum of the astrophysical black hole (the Kerr
parameter -- a representative feature of the background black hole metric)
in estimating the value of the acoustic surface gravity (the representative
feature of the corresponding analogue space time) has been investigated for
axially symmetric inflow of hydrodynamic fluid onto a rotating black hole.
Since almost all astrophysical black holes are supposed to posses some degree
of intrinsic rotation, the influence of the Kerr parameter on classical
analogue models is very important to understand.
For certain values of the initial boundary conditions describing the
aforementioned flow, more than one acoustic horizons, namely two black hole
type and one white hole type, may form, where the surface gravity may become
formally infinite at the acoustic white hole. The connection between the
corresponding analogue Hawking temperature with astrophysically relevant
observables associated with the spectral signature has been discussed.Comment: 22 pages, 11 figures, Comments welcom
Integrable deformations of the coset CFTs
We study the effective action for the integrable -deformation of the
coset CFTs. For unequal levels theses
models do not fall into the general discussion of -deformations of
CFTs corresponding to symmetric spaces and have many attractive features. We
show that the perturbation is driven by parafermion bilinears and we revisit
the derivation of their algebra. We uncover a non-trivial symmetry of these
models parametric space, which has not encountered before in the literature.
Using field theoretical methods and the effective action we compute the exact
in the deformation parameter -function and explicitly demonstrate the
existence of a fixed point in the IR corresponding to the
coset CFTs. The same result is verified
using gravitational methods for . We examine various limiting cases
previously considered in the literature and found agreement.Comment: 1+23 pages, Latex; v2: NPB version; v3: Correcting a typo in Eqs.
(2.21), (2.22
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