Graphene and the Zermelo Optical Metric of the BTZ Black Hole

It is well known that the low energy electron excitations of the curved graphene sheet $\Sigma$ are solutions of the massless Dirac equation on a 2+1 dimensional ultra-static metric on ${\Bbb R} \times \Sigma$. An externally applied electric field on the graphene sheet induces a gauge potential which could be mimicked by considering a stationary optical metric of the Zermelo form, which is conformal to the BTZ black hole when the sheet has a constant negative curvature. The Randers form of the metric can model a magnetic field, which is related by a boost to an electric one in the Zermelo frame. We also show that there is fundamental geometric obstacle to obtaining a model that extends all the way to the black hole horizon.Comment: 10 pages Latex, no figures, substantial revisions, relation between magnetic and electric fields and Randers and Zermelo forms clarifie

A genus six cyclic tetragonal reduction of the Benney equations

A reduction of Benney’s equations is constructed corresponding to Schwartz–Christoffel maps associated with a family of genus six cyclic tetragonal curves. The mapping function, a second kind Abelian integral on the associated Riemann surface, is constructed explicitly as a rational expression in derivatives of the Kleinian σ-function of the curve

On the Multiple Deaths of Whitehead's Theory of Gravity

Whitehead's 1922 theory of gravitation continues to attract the attention of philosophers, despite evidence presented in 1971 that it violates experiment. We demonstrate that the theory strongly fails five quite different experimental tests, and conclude that, notwithstanding its meritorious philosophical underpinnings, Whitehead's theory is truly dead.Comment: 22 pages; to be submitted to Studies In History And Philosophy Of Modern Physic

Gravitational Instantons, Confocal Quadrics and Separability of the Schr\"odinger and Hamilton-Jacobi equations

A hyperk\"ahler 4-metric with a triholomorphic SU(2) action gives rise to a family of confocal quadrics in Euclidean 3-space when cast in the canonical form of a hyperk\"ahler 4-metric metric with a triholomorphic circle action. Moreover, at least in the case of geodesics orthogonal to the U(1) fibres, both the covariant Schr\"odinger and the Hamilton-Jacobi equation is separable and the system integrable.Comment: 10 pages Late

A String and M-theory Origin for the Salam-Sezgin Model

An M/string-theory origin for the six-dimensional Salam-Sezgin chiral gauged supergravity is obtained, by embedding it as a consistent Pauli-type reduction of type I or heterotic supergravity on the non-compact hyperboloid ${\cal H}^{2,2}$ times $S^1$. We can also obtain embeddings of larger, non-chiral, gauged supergravities in six dimensions, whose consistent truncation yields the Salam-Sezgin theory. The lift of the Salam-Sezgin (Minkowski)$_4\times S^2$ ground state to ten dimensions is asymptotic at large distances to the near-horizon geometry of the NS5-brane.Comment: Latex, 18 pages; minor correction

A remark on kinks and time machines

We describe an elementary proof that a manifold with the topology of the Politzer time machine does not admit a nonsingular, asymptotically flat Lorentz metric.Comment: 4 page

Extended uncertainty principle and the geometry of (anti)-de Sitter space

It has been proposed that on (anti)-de Sitter background, the Heisenberg uncertainty principle should be modified by the introduction of a term proportional to the cosmological constant. We show that this modification of the uncertainty principle can be derived straightforwardly from the geometric properties of (anti)-de Sitter spacetime. We also discuss the connection between the so-called extended generalized uncertainty principle and triply special relativity.Comment: 8 pages, plain TeX, references adde

First Law of Black Rings Thermodynamics in Higher Dimensional Dilaton Gravity with p + 1 Strength Forms

We derive the first law of black rings thermodynamics in n-dimensional Einstein dilaton gravity with additional (p+1)-form field strength being the simplest generalization of five-dimensional theory containing a stationary black ring solution with dipole charge. It was done by means of choosing any cross section of the event horizon to the future of the bifurcation surface.Comment: 6 pages, to be published in Phys.Rev.D1