Multi-black holes and instantons in effective string theory

The effective action for string theory which takes into account non-minimal coupling of moduli admits multi-black hole solutions. The euclidean continuation of these solutions can be interpreted as an instanton mediating the splitting and recombination of the throat of extremal magnetically charged black holes.Comment: 10 pages, plain Te

The Decay of Magnetic Fields in Kaluza-Klein Theory

Magnetic fields in five-dimensional Kaluza-Klein theory compactified on a circle correspond to ``twisted'' identifications of five dimensional Minkowski space. We show that a five dimensional generalisation of the Kerr solution can be analytically continued to construct an instanton that gives rise to two possible decay modes of a magnetic field. One decay mode is the generalisation of the ``bubble decay" of the Kaluza-Klein vacuum described by Witten. The other decay mode, rarer for weak fields, corresponds in four dimensions to the creation of monopole-anti-monopole pairs. An instanton for the latter process is already known and is given by the analytic continuation of the \KK\ Ernst metric, which we show is identical to the five dimensional Kerr solution. We use this fact to illuminate further properties of the decay process. It appears that fundamental fermions can eliminate the bubble decay of the magnetic field, while allowing the pair production of Kaluza-Klein monopoles.Comment: 25 pages, one figure. The discussion of fermions has been revised: We show how fundamental fermions can eliminate the bubble-type instability but still allow pair creation of monopole

Non-asymptotically flat, non-AdS dilaton black holes

We show that previously known non-asymptotically flat static black hole solutions of Einstein-Maxwell-dilaton theory may be obtained as near-horizon limits of asymptotically flat black holes. Specializing to the case of the dilaton coupling constant $\alpha^2 = 3$, we generate from the non-asymptotically flat magnetostatic or electrostatic black holes two classes of rotating dyonic black hole solutions. The rotating dyonic black holes of the ``magnetic'' class are dimensional reductions of the five-dimensional Myers-Perry black holes relative to one of the azimuthal angles, while those of the ``electric'' class are twisted dimensional reductions of rotating dyonic Rasheed black strings. We compute the quasi-local mass and angular momentum of our rotating dyonic black holes, and show that they satisfy the first law of black hole thermodynamics, as well as a generalized Smarr formula. We also discuss the construction of non-asymptotically flat multi-extreme black hole configurations.Comment: Minor corrections. 2 references added. To appear in Physical Review

Moduli, Scalar Charges, and the First Law of Black Hole Thermodynamics

We show that under variation of moduli fields $\phi$ the first law of black hole thermodynamics becomes $dM = {\kappa dA\over 8\pi} + \Omega dJ + \psi dq + \chi dp - \Sigma d\phi$, where $\Sigma$ are the scalar charges. We also show that the ADM mass is extremized at fixed $A$, $J$, $(p,q)$ when the moduli fields take the fixed value $\phi_{\rm fix}(p,q)$ which depend only on electric and magnetic charges. It follows that the least mass of any black hole with fixed conserved electric and magnetic charges is given by the mass of the double-extreme black hole with these charges. Our work allows us to interpret the previously established result that for all extreme black holes the moduli fields at the horizon take a value $\phi= \phi_{\rm fix}(p,q)$ depending only on the electric and magnetic conserved charges: $\phi_{\rm fix}(p,q)$ is such that the scalar charges $\Sigma ( \phi_{\rm fix}, (p,q))=0$.Comment: 3 pages, no figures, more detailed versio

Generalized Killing equations and Taub-NUT spinning space

The generalized Killing equations for the configuration space of spinning particles (spinning space) are analysed. Simple solutions of the homogeneous part of these equations are expressed in terms of Killing-Yano tensors. The general results are applied to the case of the four-dimensional euclidean Taub-NUT manifold.Comment: 10 pages, late

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

FES rehabilitation platform with real-time control and performance feedback.

Osteoporosis after spinal cord injury is associated with low-trauma fractures, and consequently with increased risk of morbidity and mortality. The loss of bone mass density (BMD) due to paraplegia can be reduced through cyclical electrically-induced muscle contractions. Here we propose an FES control system based on posture switching, that induces transient loading of the lower limbs during a set of standing postures. This aims to produce an increased, evenly distributed BMD, whilst minimising FES-induced muscle fatigue. Here we describe the design and assessment of the FES exercising platform, comprising a controllable multi-channel electrical stimulator and an instrumented standing frame. The platform supports standing and postural shifting, provides real-time human-in-the-loop FES control with on-line feedback to the user. The platforms is used to investigate the effect of regular exercise on the distribution of BMD in people with paraplegia

Vacuum decay via Lorentzian wormholes

We speculate about the spacetime description due to the presence of Lorentzian wormholes (handles in spacetime joining two distant regions or other universes) in quantum gravity. The semiclassical rate of production of these Lorentzian wormholes in Reissner-Nordstr\"om spacetimes is calculated as a result of the spontaneous decay of vacuum due to a real tunneling configuration. In the magnetic case it only depends on the field theoretical fine structure constant. We predict that the quantum probability corresponding to the nucleation of such geodesically complete spacetimes should be actually negligible in our physical Universe

Multi-black hole solutions in five dimensions

Using a recently developed generalized Weyl formalism, we construct an asymptotically flat, static vacuum Einstein solution that describes a superposition of multiple five-dimensional Schwarzschild black holes. The spacetime exhibits a U(1)\times U(1) rotational symmetry. It is argued that for certain choices of parameters, the black holes are collinear and so may be regarded as a five-dimensional generalization of the Israel-Khan solution. The black holes are kept in equilibrium by membrane-like conical singularities along the two rotational axes; however, they still distort one another by their mutual gravitational attraction. We also generalize this solution to one describing multiple charged black holes, with fixed mass-to-charge ratio, in Einstein-Maxwell-dilaton theory.Comment: 23 pages, 6 figure

Nucleating Black Holes via Non-Orientable Instantons

We extend the analysis of black hole pair creation to include non- orientable instantons. We classify these instantons in terms of their fundamental symmetries and orientations. Many of these instantons admit the pin structure which corresponds to the fermions actually observed in nature, and so the natural objection that these manifolds do not admit spin structure may not be relevant. Furthermore, we analyse the thermodynamical properties of non-orientable black holes and find that in the non-extreme case, there are interesting modifications of the usual formulae for temperature and entropy.Comment: 27 pages LaTeX, minor typos are correcte