107 research outputs found
Cosmological Einstein-Yang-Mills equations
We use a systematic construction method for invariant connections on
homogeneous spaces to find the Einstein-SU(n)-Yang-Mills equations for
Friedmann-Robertson-Walker and locally rotationally symmetric homogeneous
cosmologies. These connections depend on the choice of a homomorphism from the
isotropy group into the gauge group. We consider here the cases of the gauge
group SU(n) and SO(n) where these homomorphisms correspond to unitary or
orthogonal representations of the isotropy group. For some of the simpler cases
the full system of the evolution equations are derived, for others we only
determine the number of dynamical variables that remain after some mild fixing
of the gauge.Comment: 28 pages, uses amsmath,amsthm,amssymb,epsfig,verbatim, minor
correction
An extrahippocampal projection from the dentate gyrus to the olfactory tubercle
Background: The dentate gyrus is well known for its mossy fiber projection to the hippocampal field 3 (CA3) and its extensive associational and commissural connections. The dentate gyrus, on the other hand, has only few projections to the CA1 and the subiculum, and none have clearly been shown to extrahippocampal target regions. Results: Using anterograde and retrograde tracer techniques in the Madagascan lesser hedgehog tenrec (Afrosoricidae, Afrotheria) it was shown in this study that the dentate hilar region gave rise to a faint, but distinct, bilateral projection to the most rostromedial portion of the olfactory tubercle, particularly its molecular layer. Unlike the CA1 and the subiculum the dentate gyrus did not project to the accumbens nucleus. A control injection into the medial septum-diagonal band complex also retrogradely labeled cells in the dentate hilus, but these neurons were found immediately adjacent to the heavily labeled CA3, while the tracer injections into the rostromedial tubercle did not reveal any labeling in CA3. Conclusion: The dentate hilar neurons projecting to the olfactory tubercle cannot be considered displaced cells of CA3 but represent true dentato-tubercular projection neurons. This projection supplements the subiculo-tubercular projection. Both terminal fields overlap among one another as well as with the fiber terminations arising in the anteromedial frontal cortex. The rostromedial olfactory tubercle might represent a distinct ventral striatal target area worth investigating in studies of the parallel processing of cortico-limbic information in tenrec as well as in cat and monkey
Topological Black Holes of (n+1)-dimensional Einstein-Yang-Mills Gravity
We present the topological solutions of Einstein gravity in the presence of a
non-Abelian Yang-Mills field. In () dimensions, we consider the
semisimple group as the Yang-Mills gauge group, and
introduce the black hole solutions with hyperbolic horizon. We argue that the
4-dimensional solution is exactly the same as the 4-dimensional solution of
Einstein-Maxwell gravity, while the higher-dimensional solutions are new. We
investigate the properties of the higher-dimensional solutions and find that
these solutions in 5 dimensions have the same properties as the topological
5-dimensional solution of Einstein-Maxwell (EM) theory although the metric
function in 5 dimensions is different. But in 6 and higher dimensions, the
topological solutions of EYM and EM gravities with non-negative mass have
different properties. First, the singularity of EYM solution does not present a
naked singularity and is spacelike, while the singularity of topological
Reissner-Nordstrom solution is timelike. Second, there are no extreme 6 or
higher-dimensional black holes in EYM gravity with non-negative mass, while
these kinds of solutions exist in EM gravity. Furthermore, EYM theory has no
static asymptotically de Sitter solution with non-negative mass, while EM
gravity has.Comment: 14 pages, 2 figures, accepted by Mod. Phys. Lett.
Topological Black Holes of Einstein-Yang-Mills dilaton Gravity
We present the topological solutions of Einstein-dilaton gravity in the
presence of a non-Abelian Yang-Mills field. In 4 dimensions, we consider the
and semisimple group as the Yang-Mills gauge group, and
introduce the black hole solutions with spherical and hyperbolic horizons,
respectively. The solution in the absence of dilaton potential is
asymptotically flat and exists only with spherical horizon. Contrary to the
non-extreme Reissner-Nordstrom black hole, which has two horizons with a
timelike and avoidable singularity, here the solution may present a black hole
with a null and unavoidable singularity with only one horizon. In the presence
of dilaton potential, the asymptotic behavior of the solutions is neither flat
nor anti-de Sitter. These solutions contain a null and avoidable singularity,
and may present a black hole with two horizons, an extreme black hole or a
naked singularity. We also calculate the mass of the solutions through the use
of a modified version of Brown and York formalism, and consider the first law
of thermodynamics.Comment: 13 pages, 3 figure
Leibnizian, Galilean and Newtonian structures of spacetime
The following three geometrical structures on a manifold are studied in
detail: (1) Leibnizian: a non-vanishing 1-form plus a Riemannian
metric \h on its annhilator vector bundle. In particular, the possible
dimensions of the automorphism group of a Leibnizian G-structure are
characterized. (2) Galilean: Leibnizian structure endowed with an affine
connection (gauge field) which parallelizes and \h. Fixed
any vector field of observers Z (), an explicit Koszul--type
formula which reconstruct bijectively all the possible 's from the
gravitational and vorticity fields
(plus eventually the torsion) is provided. (3) Newtonian: Galilean structure
with \h flat and a field of observers Z which is inertial (its flow preserves
the Leibnizian structure and ). Classical concepts in Newtonian
theory are revisited and discussed.Comment: Minor errata corrected, to appear in J. Math. Phys.; 22 pages
including a table, Late
Characterizing asymptotically anti-de Sitter black holes with abundant stable gauge field hair
In the light of the "no-hair" conjecture, we revisit stable black holes in
su(N) Einstein-Yang-Mills theory with a negative cosmological constant. These
black holes are endowed with copious amounts of gauge field hair, and we
address the question of whether these black holes can be uniquely characterized
by their mass and a set of global non-Abelian charges defined far from the
black hole. For the su(3) case, we present numerical evidence that stable black
hole configurations are fixed by their mass and two non-Abelian charges. For
general N, we argue that the mass and N-1 non-Abelian charges are sufficient to
characterize large stable black holes, in keeping with the spirit of the
"no-hair" conjecture, at least in the limit of very large magnitude
cosmological constant and for a subspace containing stable black holes (and
possibly some unstable ones as well).Comment: 33 pages, 13 figures, minor change
Slowly Rotating Non-Abelian Black Holes
It is shown that the well-known non-Abelian static SU(2) black hole solutions
have rotating generalizations, provided that the hypothesis of linearization
stability is accepted. Surprisingly, this rotating branch has an asymptotically
Abelian gauge field with an electric charge that cannot vanish, although the
non-rotating limit is uncharged. We argue that this may be related to our
second finding, namely that there are no globally regular slowly rotating
excitations of the particle-like Bartnik-McKinnon solutions.Comment: 8 pages, LaTe
Particle-Like Solutions of the Einstein-Dirac Equations
The coupled Einstein-Dirac equations for a static, spherically symmetric
system of two fermions in a singlet spinor state are derived. Using numerical
methods, we construct an infinite number of soliton-like solutions of these
equations. The stability of the solutions is analyzed. For weak coupling (i.e.,
small rest mass of the fermions), all the solutions are linearly stable (with
respect to spherically symmetric perturbations), whereas for stronger coupling,
both stable and unstable solutions exist. For the physical interpretation, we
discuss how the energy of the fermions and the (ADM) mass behave as functions
of the rest mass of the fermions. Although gravitation is not renormalizable,
our solutions of the Einstein-Dirac equations are regular and well-behaved even
for strong coupling.Comment: 31 pages, LaTeX, 21 PostScript figures, some references adde
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
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