TL;DR
This paper develops a noncommutative theory of gravity by deforming spacetime geometry and symmetries into a noncommutative framework, explicitly constructing the associated algebraic structures.
Contribution
It introduces a consistent noncommutative gravity model by twisting spacetime symmetries and defining their algebraic structures.
Findings
Deformed Lie algebra of noncommutative diffeomorphisms constructed
Explicit formulation of noncommutative Poincare' algebra provided
Foundation for noncommutative gravity theory established
Abstract
Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie algebra structure and that of infinitesimal Poincare' transformations is defined and explicitly constructed. This allows to construct a noncommutative theory of gravity.
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