This thesis establishes a precise mathematical connection between the Einstein equations of general relativity and the incompressible Navier-Stokes equation of fluid dynamics. We carry out a holographic analysis which relates solutions to the Einstein equations to the behaviour of a dual fluid living in one fewer dimensions. Gravitational systems are found to exhibit Navier-Stokes behaviour when we study the dynamics of the region near an event horizon. Thus, we find non-linear deformations of Einstein solutions which, after taking a suitable near horizon limit and imposing our particular choice of boundary conditions, turn out to be precisely characterised by solutions to the incompressible Navier-Stokes equation. In other words, for any solution to the Navier-Stokes equation, the set-up we present provides a solution to the Einstein equations near a horizon. We consider the cases of fluids flowing on the plane and on the sphere. Fluid dynamics on the plane is analysed foremost in the context of a flat background geometry whilst the spherical analysis is undertaken for Schwarzschild black holes and the static patch of four-dimensional de Sitter space. / Physics
| Identifer | oai:union.ndltd.org:harvard.edu/oai:dash.harvard.edu:1/10330319 |
| Date | January 2012 |
| Creators | Bredberg, Irene |
| Contributors | Strominger, Andrew E. |
| Publisher | Harvard University |
| Source Sets | Harvard University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Rights | closed access |
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