This project focuses on a physical and mathematical investigation of the Einstein-Euler system, a set of equations describing evolution of an ideal fluid in curved spacetime. The proposal is to use a combination of techniques from relativity, differential equations, dynamical systems and computational tools to better understand the behaviour of certain solutions to the Einstein-Euler system, generalizing when possible to fluids with viscosity—an area of current interest in Cosmology.
The plan of study will be as follows: first, the student will survey original literature on the (classical and relativistic) Euler system. In parallel, she/he will learn the Mathematica xAct package to compute symmetric reductions of the Einstein-Euler system. Using the techniques learned, it will be possible to calculate exact and/or numerical solutions of the Einstein-Euler system.
Next steps will involve the study of papers in Cosmology which introduce viscosity into the system with a fixed background spacetime (e.g., FLRW or Bianchi spacetimes). The student will investigate the Friedman equations of the viscous model using a dynamical systems approach and model the evolution equations numerically.
Depending on progress, work done in the full Einstein-Navier-Stokes system could constitute new scientific research in viscous cosmology.
