Well-posed formulation of Lovelock and Horndeski theories

Abstract: Lovelock theories are the most general diffeomorphism invariant theories of gravity in higher dimensions with second order equations of motion. Horndeski theories are the most general diffeomorphism invariant theories of gravity coupled to a scalar field in four dimensions with second order equations of motion. In this talk I will discuss well-posedness of the initial value problem for these theories. Previous work has shown that (generalised) harmonic gauge does not give a well-posed initial value problem. I will describe recent work with Aron Kovacs in which we introdued a modification of harmonic gauge that does give a well-posed initial value problem provided that the theory remains “weakly coupled”. Our modified harmonic gauge may also have applications in conventional GR.

general relativity and quantum cosmologymathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

( video )

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JoMaReC - Joint Online Mathematical Relativity Colloquium

Series comments: This monthly online colloquium is meant to be accessible to and informative for mathematicians and mathematical physicists with a background in General Relativity, widely interpreted to include Lorentzian Geometry, and Geometric Analysis of various Partial Differential Equations related to General Relativity.

It is aimed to present motivation and applications of particular results and/or introduce specific subfields, while refraining from too much technicalities.

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