Kalb-Ramond field, black holes and black strings in (2 + 1)D

Abstract: New rotating dilaton black hole and black string solutions in three spacetime dimensions are obtained. The background spacetime interpolates between Anti-de Sitter and a (an asymptotically) flat spacetime. The new black strings are characterized by their masses, angular momenta and axion charges. The uncharged black string solutions have only a single horizon. They contain a curvature singularity enclosed inside their horizons. Thus, they are also black hole solutions of Einstein-scalar gravity. On the other hand, the charged black string solutions have two horizons. They may or may not contain a curvature singularity depending on the ratio of their inner and outer horizons radii. When they contain a singularity, the singularity is either at or enclosed inside their inner horizons. We also obtain, in addition to the uncharged black strings, other new black hole solutions of Einstein-scalar gravity by applying duality transformation on the new charged black strings. The new black holes are described by their masses and angular momenta. We show that their angular momenta do not depend on their horizons radii. We also find that the masses of a class of the black holes can be made negative by adjusting, using the gauge ambiguity, the asymptotic value of the (independent component of the) Kalb-Ramond field in the dual black strings. We also discuss black hole and black string solutions with a curvature singularity at or beyond their outer or event horizons. Black hole solutions with a ring curvature singularity in between their inner and outer horizons are also presented.