A new class of obstructions to the smoothness of null infinity

Expansions of the gravitational field arising from the development of asymptotically Euclidean, time symmetric, conformally flat initial data are calculated in a neighbourhood of spatial and null infinities up to order 6. To this ends a certain representation of spatial infinity as a cylinder is used. This set up is based on the properties of conformal geodesics. It is found that these expansions suggest that null infinity has to be non-smooth unless the Newman-Penrose constants of the spacetime, and some other higher order quantities of the spacetime vanish. As a consequence of these results it is conjectured that similar conditions occur if one were to take the expansions to even higher orders. Furthermore, the smoothness conditions obtained suggest that if a time symmetric initial data which is conformally flat in a neighbourhood of spatial infinity yields a smooth null infinity, then the initial data must in fact be Schwarzschildean around spatial infinity.Comment: 24 pages, 4 figure

Topology, rigid cosymmetries and linearization instability in higher gauge theories

We consider a class of non-linear PDE systems, whose equations possess Noether identities (the equations are redundant), including non-variational systems (not coming from Lagrangian field theories), where Noether identities and infinitesimal gauge transformations need not be in bijection. We also include theories with higher stage Noether identities, known as higher gauge theories (if they are variational). Some of these systems are known to exhibit linearization instabilities: there exist exact background solutions about which a linearized solution is extendable to a family of exact solutions only if some non-linear obstruction functionals vanish. We give a general, geometric classification of a class of these linearization obstructions, which includes as special cases all known ones for relativistic field theories (vacuum Einstein, Yang-Mills, classical N=1 supergravity, etc.). Our classification shows that obstructions arise due to the simultaneous presence of rigid cosymmetries (generalized Killing condition) and non-trivial de Rham cohomology classes (spacetime topology). The classification relies on a careful analysis of the cohomologies of the on-shell Noether complex (consistent deformations), adjoint Noether complex (rigid cosymmetries) and variational bicomplex (conserved currents). An intermediate result also gives a criterion for identifying non-linearities that do not lead to linearization instabilities.Comment: v2: 33 pages, added an important reference to earlier work of Arms-Anderson, close to published versio

Does asymptotic simplicity allow for radiation near spatial infinity?

A representation of spatial infinity based in the properties of conformal geodesics is used to obtain asymptotic expansions of the gravitational field near the region where null infinity touches spatial infinity. These expansions show that generic time symmetric initial data with an analytic conformal metric at spatial infinity will give rise to developments with a certain type of logarithmic singularities at the points where null infinity and spatial infinity meet. These logarithmic singularities produce a non-smooth null infinity. The sources of the logarithmic singularities are traced back down to the initial data. It is shown that is the parts of the initial data responsible for the non-regular behaviour of the solutions are not present, then the initial data is static to a certain order. On the basis of these results it is conjectured that the only time symmetric data sets with developments having a smooth null infinity are those which are static in a neighbourhood of infinity. This conjecture generalises a previous conjecture regarding time symmetric, conformally flat data. The relation of these conjectures to Penrose's proposal for the description of the asymptotic gravitational field of isolated bodies is discussed.Comment: 22 pages, 4 figures. Typos and grammatical mistakes corrected. Version to appear in Comm. Math. Phy

Apodized Pupil Lyot Coronagraphs for Arbitrary Apertures. IV. Reduced Inner Working Angle and Increased Robustness to Low-Order Aberrations

The Apodized Pupil Lyot Coronagraph (APLC) is a diffraction suppression system installed in the recently deployed instruments Palomar/P1640, Gemini/GPI, and VLT/SPHERE to allow direct imaging and spectroscopy of circumstellar environments. Using a prolate apodization, the current implementations offer raw contrasts down to $10^{-7}$ at 0.2 arcsec from a star over a wide bandpass (20\%), in the presence of central obstruction and struts, enabling the study of young or massive gaseous planets. Observations of older or lighter companions at smaller separations would require improvements in terms of inner working angle (IWA) and contrast, but the methods originally used for these designs were not able to fully explore the parameter space. We here propose a novel approach to improve the APLC performance. Our method relies on the linear properties of the coronagraphic electric field with the apodization at any wavelength to develop numerical solutions producing coronagraphic star images with high-contrast region in broadband light. We explore the parameter space by considering different aperture geometries, contrast levels, dark-zone sizes, bandpasses, and focal plane mask sizes. We present an application of these solutions to the case of Gemini/GPI with a design delivering a $10^{-8}$ raw contrast at 0.19 arcsec and offering a significantly reduced sensitivity to low-order aberrations compared to the current implementation. Optimal solutions have also been found to reach $10^{-10}$ contrast in broadband light regardless of the telescope aperture shape (in particular the central obstruction size), with effective IWA in the $2-3.5\lambda/D$ range, therefore making the APLC a suitable option for the future exoplanet direct imagers on the ground or in space.Comment: 14 pages, 10 figures, accepted in Ap

TASI Lectures on the Cosmological Constant

The energy density of the vacuum, Lambda, is at least 60 orders of magnitude smaller than several known contributions to it. Approaches to this problem are tightly constrained by data ranging from elementary observations to precision experiments. Absent overwhelming evidence to the contrary, dark energy can only be interpreted as vacuum energy, so the venerable assumption that Lambda=0 conflicts with observation. The possibility remains that Lambda is fundamentally variable, though constant over large spacetime regions. This can explain the observed value, but only in a theory satisfying a number of restrictive kinematic and dynamical conditions. String theory offers a concrete realization through its landscape of metastable vacua.Comment: 39 pages, 3 figure

Adaptive Airborne Separation to Enable UAM Autonomy in Mixed Airspace

The excitement and promise generated by Urban Air Mobility (UAM) concepts have inspired both new entrants and large aerospace companies throughout the world to invest hundreds of millions in research and development of air vehicles, both piloted and unpiloted, to fulfill these dreams. The management and separation of all these new aircraft have received much less attention, however, and even though NASAs lead is advancing some promising concepts for Unmanned Aircraft Systems (UAS) Traffic Management (UTM), most operations today are limited to line of sight with the vehicle, airspace reservation and geofencing of individual flights. Various schemes have been proposed to control this new traffic, some modeled after conventional air traffic control and some proposing fully automatic management, either from a ground-based entity or carried out on board among the vehicles themselves. Previous work has examined vehicle-based traffic management in the very low altitude airspace within a metroplex called UTM airspace in which piloted traffic is rare. A management scheme was proposed in that work that takes advantage of the homogeneous nature of the traffic operating in UTM airspace. This paper expands that concept to include a traffic management plan usable at all altitudes desired for electric Vertical Takeoff and Landing urban and short-distance, inter-city transportation. The interactions with piloted aircraft operating under both visual and instrument flight rules are analyzed, and the role of Air Traffic Control services in the postulated mixed traffic environment is covered. Separation values that adapt to each type of traffic encounter are proposed, and the relationship between required airborne surveillance range and closure speed is given. Finally, realistic scenarios are presented illustrating how this concept can reliably handle the density and traffic mix that fully implemented and successful UAM operations would entail

On Asymptotic Flatness and Lorentz Charges

In this paper we establish two results concerning four-dimensional asymptotically flat spacetimes at spatial infinity. First, we show that the six conserved Lorentz charges are encoded in two unique, distinct, but mutually dual symmetric divergence free tensors that we construct from the equations of motion. Second, we show that integrability of Einstein's equations in the asymptotic expansion is sufficient to establish the equivalence between counter-term charges defined from the variational principle and charges defined by Ashtekar and Hansen. These results clarify earlier constructions of conserved charges in the hyperboloid representation of spatial infinity. In showing this, parity condition on the mass aspect is not needed. Along the way in establishing these results, we prove two lemmae on tensor fields on three dimensional de Sitter spacetime stated by Ashtekar-Hansen and Beig-Schmidt and state and prove three additional lemmae.Comment: 26 pages; no figures; v2: minor changes; v3: clarifications + references + a new lemma added, results unaffecte