  We study algebraic type N spacetimes in the extended new massive gravity
(NMG), considering both the Born-Infeld model (BI-NMG) and the model of NMG
with any finite order curvature corrections. We show that for these spacetimes,
the field equations of BI-NMG take the form of the massive (tensorial)
Klein-Gordon type equation, just as it happens for ordinary NMG. This fact
enables us to obtain the type N solution to BI-NMG, utilizing the general type
N solution of NMG, earlier found in our work. We also obtain type N solutions
to NMG with all finite order curvature corrections and show that, in contrast
to BI-NMG, this model admits the critical point solutions, which are
counterparts of "logarithmic" AdS pp-waves solutions of NMG.

High Energy Physics - Theory;General Relativity and Quantum Cosmology