n-DBI gravity

TL;DR

n-DBI gravity is a novel gravitational theory inspired by Dirac-Born-Infeld scalar models, featuring a foliation structure and allowing for solutions with variable cosmological constants and non-unique geometries, extending Einstein gravity solutions.

Contribution

The paper introduces n-DBI gravity, showing its solutions include Einstein solutions with a variable cosmological constant and non-uniqueness, highlighting differences from standard Einstein gravity.

Findings

Solutions include Reissner-Nordstrom-(Anti) de Sitter black holes

Cosmological constant appears as an integration constant, variable in sign and magnitude

Existence of non-unique solutions with same mass and charge distinguished by foliation invariants

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.