Geometric inequalities for initial data with symmetries

We consider a class of initial data sets (Σ,h,K) for the Einstein constraint equations which we define to be generalized Brill (GB) data. This class of data is simply connected, U(1)²-invariant, maximal, and four-dimensional with two asymptotic ends. We study the properties of GB data and in particular the topology of Σ. The GB initial data sets have applications in geometric inequalities in general relativity. We construct a mass functional M for GB initial data sets and we show:(i) the mass of any GB data is greater than or equals M, (ii) it is a non-negative functional for a broad subclass of GB data, (iii) it evaluates to the ADM mass of reduced t − φi symmetric data set, (iv) its critical points are stationary U(1)²-invariant vacuum solutions to the Einstein equations. Then we use this mass functional and prove two geometric inequalities: (1) a positive mass theorem for subclass of GB initial data which includes Myers-Perry black holes, (2) a class of local mass-angular momenta inequalities for U(1)²-invariant black holes. Finally, we construct a one-parameter family of initial data sets which we show can be seen as small deformations of the extreme Myers- Perry black hole which preserve the horizon geometry and angular momenta but have strictly greater energy.

Meating the social: sharing atiku-euiash in Sheshatshiu, Labrador

This work examines atiku-euiash (caribou meat) sharing practices in Sheshatshiu, Newfoundland and Labrador, and aims to elucidate an overarching question: how do sharing practices participate in the co-constitution of the Innu ‘social’? The ‘social’ is understood in this work as a descriptor that refers to the emergent properties of the Innu collective. The thesis is that sharing practices participate in the co-constitution of the Innu social and enact its boundaries. Inside these boundaries, atiku-euiash is more than simply a food resource: by realizing Innu values of generosity, respect and autonomy, sharing implicates the associations of human, animal, and animal masters that constitute the Innu world. Sharing is connected with the enskilment of the younger generations by their el-ders, and thus with the reproduction of Innu values through time. The ways of sharing are relevant because changes in such practices affect the constitution of the Innu social. Giv-en Euro-Canadian colonization, the Innu are in a fraught social space in which sharing is interrupted by colonization practices and values. Understanding sharing is necessary to develop policies that do not interrupt the reproduction of the Innu world This work uses several research methods: participant observation, sharing surveys, and interviews. It also uses network analysis as sharing practices leave traces of giving and receiving actions and these traces can be represented as a network of givers, receivers and circulating caribou meat. There are two main ways in which caribou is hunted and shared: household-based hunts and community-based hunts. The household-based hunts are organized by the hunters themselves, who are able and willing to hunt. Community-based hunts are completely organized and funded by the SIFN or the Innu Nation. In or-der to understand the differences in the distribution of the two hunt types, the categories of centrality and clustering are used to show how the flow of atiku-eiuash and its associ-ated realization of values and enskilment correlate with different degrees of centralization inside the sharing clusters.