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

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

Localized Activation of Bending in Proximal, Medial and Distal Regions of Sea-Urchin Sperm Flagella

Spermatozoa from the sea urchin, Colobocentrotus atratus, were partially demembranated by extraction with solutions containing Triton X-100 at a concentration which was insufficient to solubilize the membranes completely. The resulting suspension was a mixture containing some spermatozoa in which a proximal, medial, or distal portion of the flagellum was membrane-covered, while the remaining portion was naked axoneme. In reactivating solutions containing 12 µM ATP, only the naked portions of the flagellum became motile. In reactivating solutions containing 0.8 mM ADP, the membrane-covered regions became motile and beat at 6-10 beats/s, while the naked regions remained immobile, or beat very slowly at about 0.3 beat/s. Activation of membrane-covered regions in ADP solutions probably results from the membrane restricting the diffusion of ATP which is formed from ADP by the axonemal adenylate kinase. The results indicate that any region of the flagellum has the capacity for autonomous beating, and that special properties of the basal end of the flagellum are not required for bend initiation. However, the beating of different regions of the flagellum is not completely independent, for in a fair number of spermatozoa the beating of the distal, membrane-covered region in 0.8 mM ADP was intermittent, and was turned on and off in phase with the much slower bending cycle in the proximal region of naked axoneme

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

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