An analysis of Born-Infeld determinantal gravity in Weitzenbock spacetime

Abstract

The Born-Infeld theory of the gravitational field formulated in Weitzenbock spacetime is studied in detail. The action, constructed quadratically upon the torsion two-form, reduces to Einstein gravity in the low field limit where the Born-Infeld constant goes to infinity, and it is described by second order field equations for the vielbein field in $D$ spacetime dimensions. The equations of motion are derived, and a number of properties coming from them are discussed. In particular, we show that under fairly general circumstances, the equations of motion are those of Einstein's General Relativity plus an energy-momentum tensor of purely geometrical character. This tensor is obtained solely from the parallelization defining the spacetime structure, which is encoded in a set of D smooth, everywhere non-null, globally defined 1-forms. Spherical symmetry is studied as an example, and we comment on the emergence of the Schwarzschild geometry within this framework. Potential (regular) extensions of it are envisioned.

8 pages, no figures. Additional comments at the end of Sec. II. Two more references are included. Accepted in PLB

References in corpus (9)

• Born-Infeld extension of new massive gravity
• Remnant group of local Lorentz transformations in f(T) theories
• Born-Infeld gravity and its functional extensions
• c-functions in the Born-Infeld extended New Massive Gravity
• Little Rip, $\Lambda$CDM and singular dark energy cosmology from Born-Infeld-$f(R)$ gravity
• Cosmological singularities in Born-Infeld determinantal gravity
• Born-Infeld Gravity with a Massless Graviton in Four Dimensions
• Born-Infeld-Horava gravity
• Cosmology in a reduced Born-Infeld--$f(T)$ theory of gravity

Cited by in corpus (8)

• McVittie solution in f(T) gravity
• BTZ gems inside regular Born-Infeld black holes
• Matching tetrads in f(T) gravity
• Chronology protection in $f(T)$ gravity: the case of Gott's pair of moving cosmic strings
• Role of the remnant symmetries in gravitational theories based on absolute parallelism: a 2D standpoint
• Thick branes in Born-Infeld determinantal gravity in Weitzenböck spacetime
• Teleparallel Jackiw-Teitelboim gravity
• Local symmetries in $f(T)$-like models: lessons from 2D