Gravity induced by noncommutative spacetime

The talk is based on my paper with E. Beggs appearing in Class. Quantum

Gravity.

Working within a bimodule approach to noncommutative geometry, we show that

even a small amount of noncommutativity drastically constrains the moduli

space of

noncommutative metrics. In particular, the algebra [x,t]=x is forced to have

a geometry

corresponding to a gravitational source at x=0 so strong that even light

cannot

escape. This provides a non-trivial example of noncommutative Riemannian

geometry

and also serves as an introduction to some general results.