Abstract
In previous articles it has been argued that a differential calculus over a noncommutative algebra uniquely determines a gravitational field in the commutative limit and that there is a unique metric which remains as a commutative ‘shadow’. Some examples were given of metrics which resulted from a given algebra and given differential calculus. Here we aboard the inverse problem, that of constructing the algebra and the differential calculus from the commutative metric. As an example a noncommutative version of the Kasner metric is proposed which is periodic. This modified metric has a cosmological constant which can be seen to be directly related to the noncommutative structure.
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