Conserved Currents of Double Field Theory

We find the conserved current associated to invariance under generalised diffeomorphisms in double field theory. This can be used to define a generalised Komar integral. We comment on its applications to solutions, in particular to the fundamental string/pp-wave. We also discuss the current in the context of Scherk-Schwarz compactifications. We calculate the current for both the original double field theory action, corresponding to the NSNS sector alone, and for the RR sector.Comment: 30 pages + appendix, v2: belated update to match published version (typos + refs fixed, some minor comments added

Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions

We obtain some improved essentially sharp Kakeya-Nikodym estimates for eigenfunctions in two-dimensions. We obtain these by proving stronger related microlocal estimates involving a natural decomposition of phase space that is adapted to the geodesic flow.Comment: 17 pages, 2 figure

An improved method for estimating source densities using the temporal distribution of Cosmological Transients

It has been shown that the observed temporal distribution of transient events in the cosmos can be used to constrain their rate density. Here we show that the peak flux--observation time relation takes the form of a power law that is invariant to the luminosity distribution of the sources, and that the method can be greatly improved by invoking time reversal invariance and the temporal cosmological principle. We demonstrate how the method can be used to constrain distributions of transient events, by applying it to Swift gamma-ray burst data and show that the peak flux--observation time relation is in good agreement with recent estimates of source parameters. We additionally show that the intrinsic time dependence allows the method to be used as a predictive tool. Within the next year of Swift observation, we find a 50% chance of obtaining a peak flux greater than that of GRB 060017 -- the highest Swift peak flux to date -- and the same probability of detecting a burst with peak flux > 100 photons s^{-1} cm^{-2} within 6 years.Comment: Submitted to ApJ Letter