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

Sigma, tau and Abelian functions of algebraic curves

We compare and contrast three different methods for the construction of the differential relations satisfied by the fundamental Abelian functions associated with an algebraic curve. We realize these Abelian functions as logarithmic derivatives of the associated sigma function. In two of the methods, the use of the tau function, expressed in terms of the sigma function, is central to the construction of differential relations between the Abelian functions.Comment: 25 page

Bulk/Boundary Thermodynamic Equivalence, and the Bekenstein and Cosmic-Censorship Bounds for Rotating Charged AdS Black Holes

We show that one may pass from bulk to boundary thermodynamic quantities for rotating AdS black holes in arbitrary dimensions so that if the bulk quantities satisfy the first law of thermodynamics then so do the boundary CFT quantities. This corrects recent claims that boundary CFT quantities satisfying the first law may only be obtained using bulk quantities measured with respect to a certain frame rotating at infinity, and which therefore do not satisfy the first law. We show that the bulk black hole thermodynamic variables, or equivalently therefore the boundary CFT variables, do not always satisfy a Cardy-Verlinde type formula, but they do always satisfy an AdS-Bekenstein bound. The universal validity of the Bekenstein bound is a consequence of the more fundamental cosmic censorship bound, which we find to hold in all cases examined. We also find that at fixed entropy, the temperature of a rotating black hole is bounded above by that of a non-rotating black hole, in four and five dimensions, but not in six or more dimensions. We find evidence for universal upper bounds for the area of cosmological event horizons and black-hole horizons in rotating black-hole spacetimes with a positive cosmological constant.Comment: Latex, 42 page

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 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

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

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

Kleinian Geometry and the N=2 Superstring

This paper is devoted to the exploration of some of the geometrical issues raised by the $N=2$ superstring. We begin by reviewing the reasons that $\beta$-functions for the $N=2$ superstring require it to live in a four-dimensional self-dual spacetime of signature $(--++)$, together with some of the arguments as to why the only degree of freedom in the theory is that described by the gravitational field. We then move on to describe at length the geometry of flat space, and how a real version of twistor theory is relevant to it. We then describe some of the more complicated spacetimes that satisfy the $\beta$-function equations. Finally we speculate on the deeper significance of some of these spacetimes.Comment: 30 pages, AMS-Te