Solar system tests and interpretation of gauge field and Newtonian prepotential in general covariant Hořava-Lifshitz gravity

Kai Lin, Shinji Mukohyama, and Anzhong Wang
Phys. Rev. D 86, 104024 – Published 7 November 2012

Abstract

In this paper, we first study spherically symmetric, stationary vacuum configurations in general covariant theory [U(1) extension] of Hořava-Lifshitz gravity with the projectability condition and an arbitrary value of the coupling constant λ. We obtain all the solutions with the assumed symmetry in closed forms. If the gauge field A and the Newtonian prepotential φ do not directly couple to matter fields, the theory is inconsistent with solar system tests for λ1, no matter how small |λ1| is. This is shown to be true also with the most general ansatz of spherically symmetric (but not necessarily stationary) configurations. Therefore, to be consistent with observations, one needs either to find a mechanism to restrict λ precisely to its relativistic value λGR=1, or to consider A and/or φ as parts of the four-dimensional metric on which matter fields propagate. In the latter, requiring that the line element be invariant not only under the foliation-preserving diffeomorphism but also under the local U(1) transformations, we propose the replacements, NNυ(AA)/c2 and NiNi+Niφ, where υ is a dimensionless coupling constant to be constrained by observations, N and Ni are, respectively, the lapse function and shift vector, and Aφ˙+Niiφ+N(iφ)2/2. With this prescription, we show explicitly that the aforementioned solutions are consistent with solar system tests for both λ=1 and λ1, provided that |υ1|<105. From this result, the physical and geometrical interpretations of the fields A and φ become clear. However, it still remains to be understood how to obtain such a prescription from the action principle.

  • Received 16 June 2012

DOI:https://doi.org/10.1103/PhysRevD.86.104024

© 2012 American Physical Society

Authors & Affiliations

Kai Lin1,*, Shinji Mukohyama2,†, and Anzhong Wang1,3,‡

  • 1Institute for Advanced Physics and Mathematics, Zhejiang University of Technology, Hangzhou 310032, China
  • 2Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), TODIAS, the University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8583, Japan
  • 3GCAP-CASPER, Physics Department, Baylor University, Waco, Texas 76798-7316, USA

  • *K_Lin@baylor.edu
  • shinji.mukohyama@ipmu.jp
  • anzhong_wang@baylor.edu

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Issue

Vol. 86, Iss. 10 — 15 November 2012

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