**Authors:** Carlos Castro

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 [Z_{a},Z_{b}] ≠ 0. The Hermitian
metric is complex-valued with symmetric and nonsymmetric components
and there are two different complex-valued Hermitian Ricci tensors
R_{μν}, S_{μν}. 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 Z_{μ} = E_{μ}^{a} Z_{a} as noncommuting
p-brane background complex spacetime coordinates is discussed in the
conclusion, where E_{μ}^{a} is the complex vielbein associated with the Hermitian
metric G_{μν} = g_{(μν)} + ig_{[μν]} = E_{μ}^{a} Ē_{ν}^{b}
This could be one of the underlying reasons why string-theory involves gravity.

**Comments:** 11 pages, This article appeared in Phys Letts B 675, (2009) 226-230

**Download:** **PDF**

[v1] 25 Aug 2009

**Unique-IP document downloads:** 177 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful. *