Spacetimes with continuous linear isotropies II: boosts

TL;DR

This paper investigates conditions under which local boost invariance in spacetimes leads to local boost symmetry, focusing on Petrov type D and conformally flat spacetimes with specific Ricci tensor types.

Contribution

It establishes precise conditions linking local boost invariance to local boost symmetry in various classes of spacetimes, including Petrov type D and certain conformally flat cases.

Findings

LBI of Riemann tensor and its first derivative implies LBS in Petrov type D spacetimes.

Most conformally flat spacetimes also require LBI of the first derivative for LBS.

Special Ricci tensor types may need higher derivatives of curvature for symmetry.

Abstract

Conditions are found which ensure that local boost invariance (LBI), invariance under a linear boost isotropy, implies local boost symmetry (LBS), i.e. the existence of a local group of motions such that for every point $P$ in a neighbourhood there is a boost leaving $P$ fixed. It is shown that for Petrov type D spacetimes this requires LBI of the Riemann tensor and its first derivative. That is also true for most conformally flat spacetimes, but those with Ricci tensors of Segre type [1(11,1)] may require LBI of the first three derivatives of curvature to ensure LBS.