The densitized lapse ("Taub function") and the Taub time gauge in cosmology

TL;DR

This paper explores the use of the densitized lapse function, known as the Taub function, and the Taub time gauge in cosmology, revealing their roles in simplifying Einstein equations and improving initial data approaches.

Contribution

It introduces a new perspective on the densitized lapse function and the Taub time gauge, linking them to the conformal approach and minimal distortion shift vectors in cosmological models.

Findings

Densitized lapse simplifies Einstein equations to Ricci evolution equations.

The Taub time gauge aligns with symmetry-adapted metric variables.

A new minimal distortion shift gauge is proposed for generic spacetimes.

Abstract

The role of the Taub time gauge in cosmology is linked to the use of the densitized lapse function instead of the lapse function in the variational principle approach to the Einstein equations. The spatial metric variational equations then become the Ricci evolution equations, which are then supplemented by the Einstein constraints which result from the variation with respect to the densitized lapse and the usual shift vector field. In those spatially homogeneous cases where the least disconnect occurs between the general theory and the restricted symmetry scenario, the recent adjustment of the conformal approach to solving the initial value problem resulting from densitized lapse considerations is seen to be inherent in the use of symmetry-adapted metric variables. The minimal distortion shift vector field is a natural vector potential for the new York thin sandwich initial data approach to the constraints, which in this case corresponds to the diagonal spatial metric gauge. For generic spacetimes, the new approach suggests defining a new minimal distortion shift gauge which agrees with the old gauge in the Taub time gauge, but which also makes its defining differential equation agree with the vector potential equation for solving the supermomentum constraint in any time gauge.