8,723 research outputs found
Goryachev-Chaplygin, Kovalevskaya, and Brdi\v{c}ka-Eardley-Nappi-Witten pp-waves spacetimes with higher rank St\"ackel-Killing tensors
Hidden symmetries of the Goryachev-Chaplygin and Kovalevskaya gyrostats
spacetimes, as well as the Brdi\v{c}ka-Eardley-Nappi-Witten pp-waves are
studied. We find out that these spacetimes possess higher rank
St\"ackel-Killing tensors and that in the case of the pp-wave spacetimes the
symmetry group of the St\"ackel-Killing tensors is the well-known Newton-Hooke
group.Comment: 11 pages; accepted for publication in JM
Flux-Confinement in Dilatonic Cosmic Strings
We study dilaton-electrodynamics in flat spacetime and exhibit a set of
global cosmic string like solutions in which the magnetic flux is confined.
These solutions continue to exist for a small enough dilaton mass but cease to
do so above a critcal value depending on the magnetic flux. There also exist
domain wall and Dirac monopole solutions. We discuss a mechanism whereby
magnetic monopolesmight have been confined by dilaton cosmic strings during an
epoch in the early universe during which the dilaton was massless.Comment: 8 pages, DAMTP R93/3
The geometry of sound rays in a wind
We survey the close relationship between sound and light rays and geometry.
In the case where the medium is at rest, the geometry is the classical geometry
of Riemann. In the case where the medium is moving, the more general geometry
known as Finsler geometry is needed. We develop these geometries ab initio,
with examples, and in particular show how sound rays in a stratified atmosphere
with a wind can be mapped to a problem of circles and straight lines.Comment: Popular review article to appear in Contemporary Physic
The Action of Instantons with Nut Charge
We examine the effect of a non-trivial nut charge on the action of
non-compact four-dimensional instantons with a U(1) isometry. If the instanton
action is calculated by dimensionally reducing along the isometry, then the nut
charge is found to make an explicit non-zero contribution. For metrics
satisfying AF, ALF or ALE boundary conditions, the action can be expressed
entirely in terms of quantities (including the nut charge) defined on the fixed
point set of the isometry. A source (or sink) of nut charge also implies the
presence of a Misner string coordinate singularity, which will have an
important effect on the Hamiltonian of the instanton.Comment: 25 page
Bohm and Einstein-Sasaki Metrics, Black Holes and Cosmological Event Horizons
We study physical applications of the Bohm metrics, which are infinite
sequences of inhomogeneous Einstein metrics on spheres and products of spheres
of dimension 5 <= d <= 9. We prove that all the Bohm metrics on S^3 x S^2 and
S^3 x S^3 have negative eigenvalue modes of the Lichnerowicz operator and by
numerical methods we establish that Bohm metrics on S^5 have negative
eigenvalues too. We argue that all the Bohm metrics will have negative modes.
These results imply that higher-dimensional black-hole spacetimes where the
Bohm metric replaces the usual round sphere metric are classically unstable. We
also show that the stability criterion for Freund-Rubin solutions is the same
as for black-hole stability, and hence such solutions using Bohm metrics will
also be unstable. We consider possible endpoints of the instabilities, and show
that all Einstein-Sasaki manifolds give stable solutions. We show how Wick
rotation of Bohm metrics gives spacetimes that provide counterexamples to a
strict form of the Cosmic Baldness conjecture, but they are still consistent
with the intuition behind the cosmic No-Hair conjectures. We show how the
Lorentzian metrics may be created ``from nothing'' in a no-boundary setting. We
argue that Lorentzian Bohm metrics are unstable to decay to de Sitter
spacetime. We also argue that noncompact versions of the Bohm metrics have
infinitely many negative Lichernowicz modes, and we conjecture a general
relation between Lichnerowicz eigenvalues and non-uniqueness of the Dirichlet
problem for Einstein's equations.Comment: 53 pages, 11 figure
Time-Dependent Multi-Centre Solutions from New Metrics with Holonomy Sim(n-2)
The classifications of holonomy groups in Lorentzian and in Euclidean
signature are quite different. A group of interest in Lorentzian signature in n
dimensions is the maximal proper subgroup of the Lorentz group, SIM(n-2).
Ricci-flat metrics with SIM(2) holonomy were constructed by Kerr and Goldberg,
and a single four-dimensional example with a non-zero cosmological constant was
exhibited by Ghanam and Thompson. Here we reduce the problem of finding the
general -dimensional Einstein metric of SIM(n-2) holonomy, with and without
a cosmological constant, to solving a set linear generalised Laplace and
Poisson equations on an (n-2)-dimensional Einstein base manifold. Explicit
examples may be constructed in terms of generalised harmonic functions. A
dimensional reduction of these multi-centre solutions gives new time-dependent
Kaluza-Klein black holes and monopoles, including time-dependent black holes in
a cosmological background whose spatial sections have non-vanishing curvature.Comment: Typos corrected; 29 page
Black Hole Solutions of Kaluza-Klein Supergravity Theories and String Theory
We find U(1)_{E} \times U(1)_{M} non-extremal black hole solutions of
6-dimensional Kaluza-Klein supergravity theories. Extremal solutions were found
by Cveti\v{c} and Youm\cite{C-Y}. Multi black hole solutions are also
presented. After electro-magnetic duality transformation is performed, these
multi black hole solutions are mapped into the the exact solutions found by
Horowitz and Tseytlin\cite{H-T} in 5-dimensional string theory compactified
into 4-dimensions. The massless fields of this theory can be embedded into the
heterotic string theory compactified on a 6-torus. Rotating black hole
solutions can be read off those of the heterotic string theory found by
Sen\cite{Sen3}.Comment: 23 pages text(latex), a figure upon reques
Applications of the Gauss-Bonnet theorem to gravitational lensing
In this geometrical approach to gravitational lensing theory, we apply the
Gauss-Bonnet theorem to the optical metric of a lens, modelled as a static,
spherically symmetric, perfect non-relativistic fluid, in the weak deflection
limit. We find that the focusing of the light rays emerges here as a
topological effect, and we introduce a new method to calculate the deflection
angle from the Gaussian curvature of the optical metric. As examples, the
Schwarzschild lens, the Plummer sphere and the singular isothermal sphere are
discussed within this framework.Comment: 10 pages, 1 figure, IoP styl
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