Supervisor: Professor Pau Figueras
Project description:
The aim of this project is to develop a mathematical and practical understanding of how to formulate the initial value problem in higher derivative theories of gravity from the point of view of effective field theory (EFT). The theories that we are going to consider are standard general relativity supplemented by higher curvature terms, such as Riemann3. These terms naturally arise as corrections from a microscopic theory of quantum gravity, but the resulting equations of motion are of order higher than two and hence it is not clear how to formulate the initial value problem. The analogous issues arises in relativistic theories of viscous hydrodynamics. In this context, the Israel-Stewart formulation of the theory in principle allows to modify the equations of motion in a way that they are well-posed while still (supposedly) capturing the long distance physics of interest and ensuring that the local entropy increases. Can a similar formulation be devised for higher derivative theories of gravity? In a recent project we have taken the first steps in this directions and shown that it indeed seems to be possible in some particular cases. However, a general understanding is lacking and our formulation only works for a specific case. In addition, no attempt has been made to connect with the recent notions of local entropy currents in higher derivative theories of gravity. The aim of the project will be to implement a Israel-Stewart like formulation of higher derivative theories of gravity based on the electric and magnetic parts of the Weyl tensor that also takes into account the positivity of the entropy current.
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