Noncommutative Solitonic Black Hole

Abstract

We investigate solitonic black hole solutions in three dimensional noncommutative spacetime. We do this in gravity with negative cosmological constant coupled to a scalar field. Noncommutativity is realized with the Moyal product which is expanded up to first order in the noncommutativity parameter in two spatial directions. With numerical simulation we study the effect of noncommutativity by increasing the value of the noncommutativity parameter starting from commutative solutions. We find that even a regular soliton solution in the commutative case becomes a black hole solution when the noncommutativity parameter reaches a certain value.