Session S19 - Geometric and Analytic Aspects of General Relativity

Wednesday, July 21, 18:00 ~ 19:00 UTC-3

The conformal method applied to fluids (done right)

David Maxwell

University of Alaska Fairbanks, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The conformal method has long been a mainstay for the construction of initial data in general relativity. Although the method has been used productively to generate non-vacuum initial data for a number of matter models based on carefully choosing a scaling for `seed data' associated with the matter fields, the scaling begged the question of what exactly was being specified about the finally constructed initial data. In recent joint work with Isenberg, we exhibited an underlying principle that determines for a given matter model how to scale it and what is being specified. In effect, a matter field and its conjugate momentum are chosen explicitly and do not scale.

In this talk, we show how to apply this principle to perfect fluids. This is an interesting case, in part because the equations obtained differ from those found in the past by ad-hoc methods. The presentation is based on a careful analysis of the Lagrangian for fluids, and the talk will include an elementary exposition of this topic.

Joint work with Jim Isenberg (University of Oregon).

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