Born-Rigid Flow and the AdS-CFT Correspondence

This paper reviews the concepts and assumptions of rigid flow in relativistic fluid mech- anics, particularly the generalisation of the classical Herglotz-Noether theorem, that are relevant to the fluid approximation of the AdS-CFT dual of large rotating black-holes used by Bhattacharyya et al. We then give a brief outline of the recently found proof the generalised theorem.Comment: 8 page

The implications of Galilean invariance for classical point particle lagrangians

We explore the implications of the requirement of Galilean invariance for classical point particle lagrangians, in which the space is not assumed to be flat to begin with. We show that for the free, time-independent lagrangian, this requirement is equivalent to the existence of gradient Killing vectors on space, which is in turn equivalent to the condition that the space is a direct product, which is totally flat in the Galilean invariant direction. We then consider more general cases and see that there is no simple generalisation to these cases.Comment: 9 page

Differential systems, moving frames, structure-preserving submersions and geometrical problems in physics

The present work applies the theories of exterior differential systems, method of equivalence and moving frames to the study of geometrical problems arising in physics, especially the class of problems that can be described as “structure-preserving submer- sions”. A novel feature of our approach is the formulation of an algorithm which we have named “the method of involutive seeds”. By using this method, we can rapidly determine the number of free functions that we must specify in order to completely specify the problem, which we will call the “degree of arbitrariness” of the problem, and which for many physical systems is linked to the physical degree of freedom. This algorithm is especially helpful in dealing with systems with many constraints such as structure-preserving submersions. We also give other examples of calculations using this algorithm: in particular, we used it to investigate the degree of arbitrariness of the theory of general very special relativity, based on Riemannian geometry with a holonomy constraint, and thus argue that such a theory is not a suitable candidate for a physical theory. As for structure-preserving submersions, which we propose as a generalisation for Riemannian submersions to other geometrical structures, after investigating the prop- erties and degrees of arbitrariness of the general construction we use it to study the problem of flows, especially rigid flows in relativity. We generalise the classical Her- glotz–Noether theorem, which states that rotational rigid flow in Minkowski spacetime must be isometric, to all dimensions and to all conformally flat spacetimes in all di- mensions, and also to shear-free flows in conformally flat spacetimes; we generalize a partial result of the Ellis conjecture that a self-gravitating shear-free perfect fluid in geodesic motion must be either expansion-free or vorticity-free to all dimensions, and we will see clearly the origin of this result from the group structure of spacetime; we discuss an approach for the general Ellis conjecture, and show the relation between the Herglotz–Noether theorem and the Ellis conjecture; we show that for a free point particle lagrangian to have a Galilean boost symmetry, it is necessary and sufficient that we have a totally flat direction decoupled from the rest; finally, we give a rough, heuristic reasoning for why some of the Pauli reductions in which we attempt to get a larger gauge group than usually allowed from dimensional reduction are consistent

Mix and Localize: Localizing Sound Sources in Mixtures

We present a method for simultaneously localizing multiple sound sources within a visual scene. This task requires a model to both group a sound mixture into individual sources, and to associate them with a visual signal. Our method jointly solves both tasks at once, using a formulation inspired by the contrastive random walk of Jabri et al. We create a graph in which images and separated sounds correspond to nodes, and train a random walker to transition between nodes from different modalities with high return probability. The transition probabilities for this walk are determined by an audio-visual similarity metric that is learned by our model. We show through experiments with musical instruments and human speech that our model can successfully localize multiple sounds, outperforming other self-supervised methods. Project site: https://hxixixh.github.io/mix-and-localizeComment: CVPR 202