Complete Decoupling Limit of Ghost-free Massive Gravity

We present the complete form of the decoupling limit of ghost-free massive gravity with a Minkowski reference metric, including the full interactions of the helicity-1 and helicity-0 modes of the massive spin-2 field. While in the metric language the square root structure of the mass terms makes it difficult to find a simple way to write down the interactions, we show that using the vierbein formulation of massive gravity, including Stueckelberg fields for both diffeomorphism and local Lorentz symmetries, we can find an explicitly resummed expression for the helicity-1 field interactions. We clarify the equations of motion for the Lorentz Stueckelberg fields and how these generate the symmetric vierbein condition which guarantees equivalence between the vierbein and metric formulations of massive gravity.Comment: 20 pages, typos corrected, references adde

On Black Holes in Massive Gravity

In massive gravity the so-far-found black hole solutions on Minkowski space happen to convert horizons into a certain type of singularities. Here we explore whether these singularities can be avoided if space-time is not asymptotically Minkowskian. We find an exact analytic black hole (BH) solution which evades the above problem by a transition at large scales to self-induced de Sitter (dS) space-time, with the curvature scale set by the graviton mass. This solution is similar to the ones discovered by Koyama, Niz and Tasinato, and by Nieuwenhuizen, but differs in detail. The solution demonstrates that in massive GR, in the Schwarzschild coordinate system, a BH metric has to be accompanied by the St\"uckelberg fields with nontrivial backgrounds to prevent the horizons to convert into the singularities. We also find an analogous solution for a Reissner-Nordstr\"om BH on dS space. A limitation of our approach, is that we find the solutions only for specific values of the two free parameters of the theory, for which both the vector and scalar fluctuations loose their kinetic terms, however, we hope our solutions represent a broader class with better behaved perturbations.Comment: 17 LateX page

Spin-orbit torque induced dipole skyrmion motion at room temperature

We demonstrate deterministic control of dipole-field-stabilized skyrmions by means of spin-orbit torques arising from heavy transition-metal seed layers. Experiments are performed on amorphous Fe/Gd multilayers that are patterned into wires and exhibit stripe domains and dipole skyrmions at room temperature. We show that while the domain walls and skyrmions are achiral on average due to lack of Dzyaloshinskii-Moriya interactions, the N\'eel-like closure domain walls at each surface are chiral and can couple to spin-orbit torques. The current-induced domain evolutions are reported for different magnetic phases, including disordered stripe domains, coexisting stripes and dipole skyrmions and a closed packed dipole skyrmion lattice. The magnetic textures exhibit motion under current excitations with a current density ~10^8 A/m2. By comparing the motion resulting from magnetic spin textures in Fe/Gd films with different heavy transition-metal interfaces, we confirm spin currents can be used to manipulate achiral dipole skyrmions via spin-orbit torques.Comment: 23 pages, 8 figure

All metrics have curvature tensors characterised by its invariants as a limit: the \epsilon-property

We prove a generalisation of the $\epsilon$-property, namely that for any dimension and signature, a metric which is not characterised by its polynomial scalar curvature invariants, there is a frame such that the components of the curvature tensors can be arbitrary close to a certain "background". This "background" is defined by its curvature tensors: it is characterised by its curvature tensors and has the same polynomial curvature invariants as the original metric.Comment: 6 page

Sequential Fragmentation of Pleistocene Forests in an East Africa Biodiversity Hotspot: Chameleons as a Model to Track Forest History

CITATION: Measey, G. J. & Tolley, K. A. 2011. Sequential fragmentation of Pleistocene forests in an East Africa biodiversity hotspot : chameleons as a model to track forest history. PLoS ONE, 6(10): e26606, doi:10.1371/journal.pone.0026606.The original publication is available at http://journals.plos.org/plosoneBackground The Eastern Arc Mountains (EAM) is an example of naturally fragmented tropical forests, which contain one of the highest known concentrations of endemic plants and vertebrates. Numerous paleo-climatic studies have not provided direct evidence for ancient presence of Pleistocene forests, particularly in the regions in which savannah presently occurs. Knowledge of the last period when forests connected EAM would provide a sound basis for hypothesis testing of vicariance and dispersal models of speciation. Dated phylogenies have revealed complex patterns throughout EAM, so we investigated divergence times of forest fauna on four montane isolates in close proximity to determine whether forest break-up was most likely to have been simultaneous or sequential, using population genetics of a forest restricted arboreal chameleon, Kinyongia boehmei. Methodology/Principal Findings We used mitochondrial and nuclear genetic sequence data and mutation rates from a fossil-calibrated phylogeny to estimate divergence times between montane isolates using a coalescent approach. We found that chameleons on all mountains are most likely to have diverged sequentially within the Pleistocene from 0.93–0.59 Ma (95% HPD 0.22–1.84 Ma). In addition, post-hoc tests on chameleons on the largest montane isolate suggest a population expansion ∼182 Ka. Conclusions/Significance Sequential divergence is most likely to have occurred after the last of three wet periods within the arid Plio-Pleistocene era, but was not correlated with inter-montane distance. We speculate that forest connection persisted due to riparian corridors regardless of proximity, highlighting their importance in the region's historic dispersal events. The population expansion coincides with nearby volcanic activity, which may also explain the relative paucity of the Taita's endemic fauna. Our study shows that forest chameleons are an apposite group to track forest fragmentation, with the inference that forest extended between some EAM during the Pleistocene 1.1–0.9 Ma.http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0026606Publisher's versio