Almost Special Holonomy in Type IIA&M Theory

We consider spaces M_7 and M_8 of G_2 holonomy and Spin(7) holonomy in seven and eight dimensions, with a U(1) isometry. For metrics where the length of the associated circle is everywhere finite and non-zero, one can perform a Kaluza-Klein reduction of supersymmetric M-theory solutions (Minkowksi)_4\times M_7 or (Minkowksi)_3\times M_8, to give supersymmetric solutions (Minkowksi)_4\times Y_6 or (Minkowksi)_3\times Y_7 in type IIA string theory with a non-singular dilaton. We study the associated six-dimensional and seven-dimensional spaces Y_6 and Y_7 perturbatively in the regime where the string coupling is weak but still non-zero, for which the metrics remain Ricci-flat but that they no longer have special holonomy, at the linearised level. In fact they have ``almost special holonomy,'' which for the case of Y_6 means almost Kahler, together with a further condition. For Y_7 we are led to introduce the notion of an ``almost G_2 manifold,'' for which the associative 3-form is closed but not co-closed. We obtain explicit classes of non-singular metrics of almost special holonomy, associated with the near Gromov-Hausdorff limits of families of complete non-singular G_2 and Spin(7) metrics.Comment: Latex, 26 page

HLA-B27 Positivity: associated health implications

HLA-B27 positivity makes the onset of autoimmune diseases such as uveitis, ankylosing spondylitis and Crohn's disease more likely to occur. Ankylosing spondylitis and Crohn's disease are two types of HLA-B27 positive diseases that demonstrate a direct association with uveitis. Although the possession of HLA-B27 positivity is not mandatory for autoimmune diseases such as uveitis to occur, HLA-B27 positivity not only makes it more likely but may modify the clinical picture in which a patient presents. In relation to assessment and diagnosis it is imperative that the medical history of patients is thoroughly examined to ensure pathological sequelae are appropriately treated. Nurses play an important role in assessing patients that have uveitis and should suspect ankylosing spondylitis or Crohn's disease may be present

Electrodynamics of Black Holes in STU Supergravity

External magnetic fields can probe the composite structure of black holes in string theory. With this motivation we study magnetised four-charge black holes in the STU model, a consistent truncation of maximally supersymmetric supergravity with four types of electromagnetic fields. We employ solution generating techniques to obtain Melvin backgrounds, and black holes in these backgrounds. For an initially electrically charged static black hole immersed in magnetic fields, we calculate the resultant angular momenta and analyse their global structure. Examples are given for which the ergoregion does not extend to infinity. We calculate magnetic moments and gyromagnetic ratios via Larmor's formula. Our results are consistent with earlier special cases. A scaling limit and associated subtracted geometry in a single surviving magnetic field is shown to lift to $AdS_3\times S^2$. Magnetizing magnetically charged black holes give static solutions with conical singularities representing strings or struts holding the black holes against magnetic forces. In some cases it is possible to balance these magnetic forces.Comment: 31 page

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

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