Classical GR as a topological theory with linear constraints

We investigate a formulation of continuum 4d gravity in terms of a constrained topological (BF) theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum gravity. We identify both the continuum version of the linear simplicity constraints used in the quantum discrete context and a linear version of the quadratic volume constraints that are necessary to complete the reduction from the topological theory to gravity. We illustrate and discuss also the discrete counterpart of the same continuum linear constraints. Moreover, we show under which additional conditions the discrete volume constraints follow from the simplicity constraints, thus playing the role of secondary constraints. Our analysis clarifies how the discrete constructions of spin foam models are related to a continuum theory with an action principle that is equivalent to general relativity.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting 2010 (ERE2010, Granada, Spain

Classical GR as a topological theory with linear constraints

We investigate a formulation of continuum 4d gravity in terms of a constrained topological (BF) theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum gravity. We identify both the continuum version of the linear simplicity constraints used in the quantum discrete context and a linear version of the quadratic volume constraints that are necessary to complete the reduction from the topological theory to gravity. We illustrate and discuss also the discrete counterpart of the same continuum linear constraints. Moreover, we show under which additional conditions the discrete volume constraints follow from the simplicity constraints, thus playing the role of secondary constraints. Our analysis clarifies how the discrete constructions of spin foam models are related to a continuum theory with an action principle that is equivalent to general relativity.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting 2010 (ERE2010, Granada, Spain

Classical GR as a topological theory with linear constraints

We investigate a formulation of continuum 4d gravity in terms of a constrained topological (BF) theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum gravity. We identify both the continuum version of the linear simplicity constraints used in the quantum discrete context and a linear version of the quadratic volume constraints that are necessary to complete the reduction from the topological theory to gravity. We illustrate and discuss also the discrete counterpart of the same continuum linear constraints. Moreover, we show under which additional conditions the discrete volume constraints follow from the simplicity constraints, thus playing the role of secondary constraints. Our analysis clarifies how the discrete constructions of spin foam models are related to a continuum theory with an action principle that is equivalent to general relativity.Comment: 4 pages, based on a talk given at the Spanish Relativity Meeting 2010 (ERE2010, Granada, Spain

The structure of frontoparallel haptic space is task dependent

In three experiments, we investigated the structure of frontoparallel haptic space. In the first experiment, we asked blindfolded participants to rotate a matching bar so that it felt parallel to the reference bar, the bars could be at various positions in the frontoparallel plane. Large systematic errors were observed, in which orientations that were perceived to be parallel were not physically parallel. In two subsequent experiments, we investigated the origin of these errors. In Experiment 2, we asked participants to verbally report the orientation of haptically presented bars. In this task, participants made errors that were considerably smaller than those made in Experiment 1. In Experiment 3, we asked participants to set bars in a verbally instructed orientation, and they also made errors significantly smaller than those observed in Experiment 1. The data suggest that the errors in the matching task originate from the transfer of the reference orientation to the matching-bar position

Dust-grain processing in circumbinary discs around evolved binaries. The RV Tauri spectral twins RU Cen and AC Her

Context: We study the structure and evolution of circumstellar discs around evolved binaries and their impact on the evolution of the central system. Aims: To study in detail the binary nature of RUCen and ACHer, as well as the structure and mineralogy of the circumstellar environment. Methods: We combine multi-wavelength observations with a 2D radiative transfer study. Our radial velocity program studies the central stars, while our Spitzer spectra and broad-band SEDs are used to constrain mineralogy, grain sizes and physical structure of the circumstellar environment. Results: We determine the orbital elements of RUCen showing that the orbit is highly eccentric with a rather long period of 1500 days. The infrared spectra of both objects are very similar and the spectral dust features are dominated by Mg-rich crystalline silicates. The small peak-to-continuum ratios are interpreted as being due to large grains. Our model contains two components with a cold midplain dominated by large grains, and the near- and mid-IR which is dominated by the emission of smaller silicates. The infrared excess is well modelled assuming a hydrostatic passive irradiated disc. The profile-fitting of the dust resonances shows that the grains must be very irregular. Conclusions: These two prototypical RVTauri pulsators with circumstellar dust are binaries where the dust is trapped in a stable disc. The mineralogy and grain sizes show that the dust is highly processed, both in crystallinity and grain size. The cool crystals show that either radial mixing is very efficient and/or that the thermal history at grain formation has been very different from that in outflows. The physical processes governing the structure of these discs are similar to those observed in protoplanetary discs around young stellar objects.Comment: 11 pages, 12 figures, accepted for publication by A&

Cosmological evolution as squeezing: a toy model for group field cosmology

We present a simple model of quantum cosmology based on the group field theory (GFT) approach to quantum gravity. The model is formulated on a subspace of the GFT Fock space for the quanta of geometry, with a fixed volume per quantum. In this Hilbert space, cosmological expansion corresponds to the generation of new quanta. Our main insight is that the evolution of a flat Friedmann–Lemaître–Robertson–Walker universe with a massless scalar field can be described on this Hilbert space as squeezing, familiar from quantum optics. As in GFT cosmology, we find that the three-volume satisfies an effective Friedmann equation similar to the one of loop quantum cosmology, connecting the classical contracting and expanding solutions by a quantum bounce. The only free parameter in the model is identified with Newton’s constant. We also comment on the possible topological interpretation of our squeezed states. This paper can serve as an introduction into the main ideas of GFT cosmology without requiring the full GFT formalism; our results can also motivate new developments in GFT and its cosmological application

Subchondral bone density distribution of the talus in clinically normal Labrador Retrievers

Background: Bones continually adapt their morphology to their load bearing function. At the level of the subchondral bone, the density distribution is highly correlated with the loading distribution of the joint. Therefore, subchondral bone density distribution can be used to study joint biomechanics non-invasively. In addition physiological and pathological joint loading is an important aspect of orthopaedic disease, and research focusing on joint biomechanics will benefit veterinary orthopaedics. This study was conducted to evaluate density distribution in the subchondral bone of the canine talus, as a parameter reflecting the long-term joint loading in the tarsocrural joint. Results: Two main density maxima were found, one proximally on the medial trochlear ridge and one distally on the lateral trochlear ridge. All joints showed very similar density distribution patterns and no significant differences were found in the localisation of the density maxima between left and right limbs and between dogs. Conclusions: Based on the density distribution the lateral trochlear ridge is most likely subjected to highest loads within the tarsocrural joint. The joint loading distribution is very similar between dogs of the same breed. In addition, the joint loading distribution supports previous suggestions of the important role of biomechanics in the development of OC lesions in the tarsus. Important benefits of computed tomographic osteoabsorptiometry (CTOAM), i.e. the possibility of in vivo imaging and temporal evaluation, make this technique a valuable addition to the field of veterinary orthopaedic research