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

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

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

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 $n$-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

Compactifications of Deformed Conifolds, Branes and the Geometry of Qubits

We present three families of exact, cohomogeneity-one Einstein metrics in $(2n+2)$ dimensions, which are generalizations of the Stenzel construction of Ricci-flat metrics to those with a positive cosmological constant. The first family of solutions are Fubini-Study metrics on the complex projective spaces $CP^{n+1}$, written in a Stenzel form, whose principal orbits are the Stiefel manifolds $V_2(R ^{n+2})=SO(n+2)/SO(n)$ divided by $Z_2$. The second family are also Einstein-K\"ahler metrics, now on the Grassmannian manifolds $G_2(R^{n+3})=SO(n+3)/((SO(n+1)\times SO(2))$, whose principal orbits are the Stiefel manifolds $V_2(R^{n+2})$ (with no $Z_2$ factoring in this case). The third family are Einstein metrics on the product manifolds $S^{n+1}\times S^{n+1}$, and are K\"ahler only for $n=1$. Some of these metrics are believed to play a role in studies of consistent string theory compactifications and in the context of the AdS/CFT correspondence. We also elaborate on the geometric approach to quantum mechanics based on the K\"ahler geometry of Fubini-Study metrics on $CP^{n+1}$, and we apply the formalism to study the quantum entanglement of qubits.Comment: 31 page

Conformal Carroll groups

Conformal extensions of Levy-Leblond's Carroll group, based on geometric properties analogous to those of Newton-Cartan space-time are proposed. The extensions are labelled by an integer $k$. This framework includes and extends our recent study of the Bondi-Metzner-Sachs (BMS) and Newman-Unti (NU) groups. The relation to Conformal Galilei groups is clarified. Conformal Carroll symmetry is illustrated by "Carrollian photons". Motion both in the Newton-Cartan and Carroll spaces may be related to that of strings in the Bargmann space.Comment: 31 pages, no figures. Minor misprints corrected and clarifications added. To be published in J. Phys.