n-DBI gravity

Carlos Herdeiro, Shinji Hirano, and Yuki Sato
Phys. Rev. D 84, 124048 – Published 27 December 2011

Abstract

n-DBI gravity is a gravitational theory introduced in [C. Herdeiro and S. Hirano, arXiv:1109.1468.], motivated by Dirac-Born-Infeld type conformal scalar theory and designed to yield noneternal inflation spontaneously. It contains a foliation structure provided by an everywhere timelike vector field n, which couples to the gravitational sector of the theory, but decouples in the small curvature limit. We show that any solution of Einstein gravity with a particular curvature property is a solution of n-DBI gravity. Among them is a class of geometries isometric to a Reissner-Nordström–(anti)-de Sitter black hole, which is obtained within the spherically symmetric solutions of n-DBI gravity minimally coupled to the Maxwell field. These solutions have, however, two distinct features from their Einstein gravity counterparts: (1) the cosmological constant appears as an integration constant and can be positive, negative, or vanishing, making it a variable quantity of the theory; and (2) there is a nonuniqueness of solutions with the same total mass, charge, and effective cosmological constant. Such inequivalent solutions cannot be mapped to each other by a foliation preserving diffeomorphism. Physically they are distinguished by the expansion and shear of the congruence tangent to n, which define scalar invariants on each leaf of the foliation.

  • Received 10 October 2011

DOI:https://doi.org/10.1103/PhysRevD.84.124048

© 2011 American Physical Society

Authors & Affiliations

Carlos Herdeiro1,*, Shinji Hirano2,†, and Yuki Sato2,3,‡

  • 1Departamento de Física, Universidade de Aveiro and I3N Campus de Santiago, 3810-183 Aveiro, Portugal
  • 2Department of Physics, Nagoya University, Nagoya 464-8602, Japan
  • 3The Niels Bohr Institute, Blegdamsvej 17, DK-2100, Copenhagen, Denmark

  • *herdeiro@ua.pt
  • hirano@eken.phys.nagoya-u.ac.jp
  • ysato@th.phys.nagoya-u.ac.jp

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Issue

Vol. 84, Iss. 12 — 15 December 2011

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