On Born's deformed reciprocal complex gravitational theory and noncommutative gravity

Abstract:

Born's reciprocal relativity in flat spacetimes is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born's theory to the case of curved spacetimes and construct a deformed Born reciprocal general relativity theory in curved spacetimes (without the need to introduce star products) as a local gauge theory of the deformed Quaplectic group that is given by the semi-direct product of U (1, 3) with the deformed (noncommutative) Weyl-Heisenberg group corresponding to noncommutative generators [Za, Zb] ≠ 0. The Hermitian metric is complex-valued with symmetric and nonsymmetric components and there are two different complex-valued Hermitian Ricci tensors Rμ ν, Sμ ν. The deformed Born's reciprocal gravitational action linear in the Ricci scalars R, S with Torsion-squared terms and BF terms is presented. The plausible interpretation of Zμ = Eμa Za as noncommuting p-brane background complex spacetime coordinates is discussed in the conclusion, where Eμa is the complex vielbein associated with the Hermitian metric Gμ ν = g(μ ν) + i g[μ ν] = Eμa over(E, ̄)νb ηa b. This could be one of the underlying reasons why string-theory involves gravity. © 2008 Elsevier B.V. All rights reserved.

Año de publicación:

2008

Keywords:

Fuente:

scopus