n-DBI gravity

Carlos Herdeiro; Shinji Hirano; Yuki Sato

doi:10.1103/physrevd.84.124048

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arXiv · 1110.0832

n-DBI gravity

Carlos Herdeiro·Shinji Hirano·Yuki Sato

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Abstract

n-DBI gravity is a gravitational theory introduced in arXiv:1109.1468 [hep-th], motivated by Dirac-Born-Infeld type conformal scalar theory and designed to yield non-eternal inflation spontaneously. It contains a foliation structure provided by an everywhere time-like 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. Amongst them is a class of geometries isometric to Reissner-Nordstrom-(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; 2) there is a non-uniqueness 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 leave of the foliation.

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Carlos Herdeiro, Shinji Hirano, Yuki Sato. 2011-10-04. n-DBI gravity. https://doi.org/10.1103/physrevd.84.124048

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