Symmetry restriction and its application to gravity

TL;DR

This paper develops a method to impose symmetry restrictions in Hamiltonian systems, simplifying calculations in gravity, especially in cosmological models like Robertson-Walker, with potential applications in quantum gravity.

Contribution

It introduces a precise symmetry restriction procedure in the Hamiltonian framework, facilitating the reduction from infinite to finite-dimensional phase spaces in gravity theories.

Findings

Provides a symmetry restriction method applicable to gravity

Demonstrates the method on Robertson-Walker cosmologies

Extends the approach to quantum gravity scenarios

Abstract

In the Hamiltonian formulation, it is not a priori clear whether a symmetric configuration will keep its symmetry during evolution. In this paper, we give precise requirements of when this is the case and propose a symmetry restriction to the phase space of the symmetric variables. This can often ease computation, especially when transcending from the infinite dimensional phase space of a field theory to a possibly finite dimensional subspace. We will demonstrate this in the case of gravity. A prominent example is the restriction of full Hamiltonian general relativity to the cosmological configurations of Robertson-Walker type. We will demonstrate our procedure in this setting and extend it to examples which appear useful in certain approaches to quantum gravity.