Non-Relativistic Gravity and the Fluid/Gravity Correspondence

Explore a comprehensive lecture on non-relativistic gravity and its relationship to fluid dynamics. The talk reviews the covariant 1/c expansion of general relativity, explaining how expanding the Einstein-Hilbert action to next-to-next-to-leading order produces non-relativistic gravity theory. Learn about this theory's formulation using Newton-Cartan geometry, which provides a covariant description of Newtonian gravity while incorporating gravitational time dilation and spatial curvature. Discover how adding a negative cosmological constant creates a non-relativistic Anti-de Sitter vacuum with a boundary defining a conformal class of Newton-Cartan geometries, and how this framework enables the construction of planar excitations corresponding to a fluid energy-momentum tensor on the boundary.