33,350 research outputs found
S-Duality for Linearized Gravity
We develope the analogue of S-duality for linearized gravity in
(3+1)-dimensions. Our basic idea is to consider the self-dual (anti-self-dual)
curvature tensor for linearized gravity in the context of the
Macdowell-Mansouri formalism. We find that the strong-weak coupling duality for
linearized gravity is an exact symmetry and implies small-large duality for the
cosmological constant.Comment: 18 pages, Latex, to be published in Phys. Lett.
Duality in cosmological perturbation theory
Cosmological perturbation equations derived from low-energy effective actions
are shown to be invariant under a duality transformation reminiscent of
electric-magnetic, strong-weak coupling, S-duality. A manifestly
duality-invariant approximation for perturbations far outside the horizon is
introduced, and it is argued to be useful even during a high curvature epoch.
Duality manifests itself through a remnant symmetry acting on the classical
moduli of cosmological models, and implying lower bounds on the number and
energy density of produced particles.Comment: 14 pages, LATEX, no figure
Electromagnetic duality in general relativity
By resolving the Riemann curvature relative to a unit timelike vector into
electric and magnetic parts, we consider duality relations analogous to the
electromagnetic theory. It turns out that the duality symmetry of the Einstein
action implies the Einstein vacuum equation without the cosmological term. The
vacuum equation is invariant under interchange of active and passive electric
parts giving rise to the same vacuum solutions but the gravitational constant
changes sign. Further by modifying the equation it is possible to construct
interesting dual solutions to vacuum as well as to flat spacetimes.Comment: 18 pages, LaTEX versio
Axisymmetric metrics in arbitrary dimensions
We consider axially symmetric static metrics in arbitrary dimension, both
with and without a cosmological constant. The most obvious such solutions have
an SO(n) group of Killing vectors representing the axial symmetry, although one
can also consider abelian groups which represent a flat `internal space'. We
relate such metrics to lower dimensional dilatonic cosmological metrics with a
Liouville potential. We also develop a duality relation between vacuum
solutions with internal curvature and those with zero internal curvature but a
cosmological constant. This duality relation gives a solution generating
technique permitting the mapping of different spacetimes. We give a large class
of solutions to the vacuum or cosmological constant spacetimes. We comment on
the extension of the C-metric to higher dimensions and provide a novel solution
for a braneworld black hole.Comment: 36 pages, LaTeX (JHEP), 4 figures, section added (published version
Charged Black Cosmic String
Global U(1) strings with cylindrical symmetry are studied in anti-de Sitter
spacetime. According as the magnitude of negative cosmological constant, they
form regular global cosmic strings, extremal black cosmic strings and charged
black cosmic strings, but no curvature singularity is involved. The
relationship between the topological charge of a neutral global string and the
black hole charge is clarified by duality transformation. Physical relevance as
straight string is briefly discussed.Comment: ll pages, LaTe
Duality in Einstein's Gravity
We show that the Einstein equations in the vacuum are invariant under an
duality symmetry which rotates the curvature 2-form into its tangent
space Hodge dual. Akin to electric-magnetic duality in gauge theory, the
duality operation maps classical solutions into each other. As an example, we
demonstrate that the Kerr solution is non-linearly mapped by duality into
Kerr-Taub-NUT.Comment: v2: references adde
On the conformal transformation and duality in gravity
The theory described by the sum of the Einstein-Hilbert action and the action
of conformal scalar field possesses the duality symmetry which includes some
special conformal transformation of the metric, and also inversion of scalar
field and of the gravitational constant. In the present paper the conformal
duality is generalized for arbitrary space-time dimension and for
the general sigma-model type conformal scalar theory. We also consider to apply
the conformal duality for the investigation of quantum gravity in the strong
curvature regime. The trace of the first coefficient of the Schwinger-DeWitt
expansion is derived and it's dependence on the gauge fixing condition is
considered. After that we discuss the way to extract the gauge-fixing
independent result and also it's possible physical applications.Comment: LaTeX, 15 pages, no figures. To appear in Classical and Quantum
Gravit
Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons and Mirror Symmetry
We address the issue why Calabi-Yau manifolds exist with a mirror pair. We
observe that the irreducible spinor representation of the Lorentz group Spin(6)
requires us to consider the vector spaces of two-forms and four-forms on an
equal footing. The doubling of the two-form vector space due to the Hodge
duality doubles the variety of six-dimensional spin manifolds. We explore how
the doubling is related to the mirror symmetry of Calabi-Yau manifolds. Via the
gauge theory formulation of six-dimensional Riemannian manifolds, we show that
the curvature tensor of a Calabi-Yau manifold satisfies the Hermitian
Yang-Mills equations on the Calabi-Yau manifold. Therefore the mirror symmetry
of Calabi-Yau manifolds can be recast as the mirror pair of Hermitian
Yang-Mills instantons. We discuss the mirror symmetry from the gauge theory
perspective.Comment: v5; 49 pages, version to appear in Advances in High Energy Physic
- …