Gravity with a dynamical preferred frame

2000/07/14 by Ted Jacobson, David Mattingly · 1 voice · 77 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #hep-ph #hep-th

paper · pdf · doi:10.1103/physrevd.64.024028

published as Phys.Rev. D64 (2001) 024028 · 9 pages; title changed, references added, relation to prior work of Gasperini discussed, errors in scalar field stress tensor corrected, various minor changes to Introduction; Final version to be published in PRD: relation to prior work of Kostelecky and Samuel spelled out in detail, clarifications and sign errors corrected in section on linearized solutions, references added; Really final version: (u^m \nabla_m u^a)^2 term added to most general Lagrangian eqn.(3.1)

arxiv published 2000/07/14 · arxiv created 2001/06/02 · arxiv updated 2001/06/02 · openalex publication_date 2001/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We study a generally covariant model in which local Lorentz invariance is broken by a dynamical unit timelike vector field u^a---the ``aether.'' Such a model makes it possible to study the gravitational and cosmological consequences of preferred frame effects, such as ``variable speed of light'' or high frequency dispersion, while preserving a generally covariant metric theory of gravity. In this paper we restrict attention to an action for an effective theory of the aether which involves only the antisymmetrized derivative \ensuremath∇_[au_b]. Without matter this theory is equivalent to a sector of the Einstein-Maxwell-charged dust system. The aether has two massless transverse excitations, and the solutions of the model include all vacuum solutions of general relativity (as well as other solutions). However, the aether generally develops gradient singularities which signal a breakdown of this effective theory. Including the symmetrized derivative in the action for the aether field may cure this problem.

Citations

• A comment on trans-Planckian physics in inflationary universe
• Generally covariant model of a scalar field with high frequency dispersion and the cosmological horizon problem

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Discussions

• You might be interested in work on 'Einstein-aether theories', which have a Lagrangian involving a metric and a unit timelike vector field. You can see many papers on the arXiv, but Ted Jacobson helpe [bsky, 2 points, 0 comments]