On noncommutative dynamic spacetimes

Abstract

Noncommutative gravity is a theory of quantum gravity that presupposes a fuzziness in spatial coordinates. Under the formalism of coherent states, mass is diffused per a gaussian distribution. In this work we begin with a review of existing noncommutative spacetime solutions. We then study the classical Vaidya spacetime with parameters for mass and charge, in the context of noncommutative gravity. The characteristic behaviour of this spacetime is discussed, with particular attention to the moment of formation of the apparent horizon. At this moment, the black hole is extremal, and we discuss the relationship between the mass and charge parameters, and the time and position of the apparent horizon. We follow with a calculation of the stress-energy tensor for a noncommutative Vaidya spacetime, and show violation of the energy conditions. Using a polytropic-like equation of state, we construct a new dynamic spacetime solution that satisfies the dominant energy condition, and encompasses several interpretations via parameter choice.