The coset formulation of gravitational theories: understanding metric-preserving changes of basis

Abstract: The requirement of distant parallelism implicitly defines a field of orthonormal frame bases. Such fields are related by a local Lorentz group, I(u). Meanwhile, changes of coordinate basis form a wider group of general linear transformations, J(u). From this, it can easily be shown that the degrees of freedom contained in the metric are the parameters of the coset space J/I. This separation of the parallelism degrees of freedom from the metric degrees of freedom allows a Cartan decomposition of the Weitzenböck connection. Holonomic frames, in which the Weitzenböck spin connection vanishes, are then found to be ones in which the frame basis is related to the coordinate basis by a transformation matrix only containing metric degrees of freedom. The transformation laws of such matrices – coset space representatives – mean that this gauge choice is not consistent with general covariance. This formulation allows the correct relationship between inertial effects and transformations in I(u) to be explored and identified. [The presentation is based on Sections 1-5 of arXiv:2211.07586. It is an extended and rearranged version of that given to the Geometric Foundations of Gravity 2021 conference.]

astrophysicscondensed mattergeneral relativity and quantum cosmologyhigh energy physicsmathematical physicsclassical physicsgeneral physics

Audience: researchers in the topic

Theoretical physics seminar @ Tartu