On the resolution of space-time singularities II

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. © 2004 Taylor & Francis Group, LLC.