n -DBI gravity
2011; American Physical Society; Volume: 84; Issue: 12 Linguagem: Inglês
10.1103/physrevd.84.124048
ISSN1550-7998
AutoresCarlos Herdeiro, Shinji Hirano, Yūki Sato,
Tópico(s)Noncommutative and Quantum Gravity Theories
Resumo$n$-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 $\mathbf{n}$, 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-Nordstr\"om--(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 $\mathbf{n}$, which define scalar invariants on each leaf of the foliation.
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