Level: MSci, MSc
Title: Relativistic fluids: exact solutions and associated dynamics
Supervisor:

Dr Shabnam Beheshti
Research Area: Geometry and Analysis
Description:

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.
Further Reading:
  • C. Misner, K. Thorne and J. Wheeler, Gravitation. WH Freeman New York, 1973.
  • L. Rezzolla and O. Zanotti, Relativistic Hydrodynamics. Oxford Univ. Press, 2013.
  • M. Disconzi, T. Kepart and R. Scherrer, A New Approach to Cosmological Bulk Viscosity, Phys. Rev. D 91 043532 (2014) https://arxiv.org/abs/1409.4918.
  • S. Beheshti, Notes on viscosity for Bianchi backgrounds [to be provided].
  • LTCC Course Notes on Dynamical Systems in Cosmology [see http://www.ltcc.ac.uk/timetable/].
Key Modules:

MTH5102 Calculus III

MTH6132 Relativity
Other Information:

Knowledge of Mathematica (or willingness to learn) is required for this project.
Current Availability: Yes