Spacetimes with continuous linear isotropies II: boosts

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.

Title amended. This is the 'author's accepted manuscript'. To appear in General Relativity and Gravitation. In press. Paper I also in press. Paper III will follow

References in corpus (2)

• Spacetimes with continuous linear isotropies I: spatial rotations
• Locally Boost Isotropic Spacetimes and the Type ${\mathbf{D}}^k$ Condition