Slides of 5 lectures at XV Brazilian School on Cosmology and ...

Korzyński’s covariant coarse-grainingIsometrically embed the boundary <strong>of</strong> a comovingdust-filled domain (with S 2 topology, positive scalarcurv<strong>at</strong>ure) into a three-dimensional Euclidean spaceConstruct a “fictitious” 3-dimensional fluid velocity whichinduces the same infinitesimal metric deform<strong>at</strong>ion onthe embedded surface as “true” flow on domainboundary original spacetimeUse velocity field to uniquely assign coarse-grainedexpressions for the volume expansion and shear.Using pushforward <strong>of</strong> ADM shift vector similarly obtain acoarse-grained vorticity.Coarse-grained quantities are quasilocal functionalswhich depend only on the geometry <strong>of</strong> the domainboundary. Class. Quan. Grav. 27 (2010) 10501515th <strong>Brazilian</strong> <strong>School</strong> on Cosmology and Gravit<strong>at</strong>ion, August 2012 – p.23/143