  One of the most debated subjects in Astronomy since the discovery of
exoplanets is how can we distinguish the most massive of such objects from
very-low mass stars like Brown Dwarfs (BDs)? We have been looking for evidences
of a difference in physical characteristics that could be related to different
formation processes. Using a new diagnostic diagram that compares the baryonic
gravitational potential (BGP) with the distances from their host stars, we have
classified a sample of 355 well-studied exoplanets according to their possible
structures. We have then compared the exoplanets to a sample of 87 confirmed
BDs, identifying a range in BGP that could be common to both objects. By
analyzing the mass-radius relations (MRR) of the exoplanets and BDs in those
different BGP ranges, we were able to distinguish different characteristic
behaviors. By comparing with models in the literature, our results suggest that
BDs and massive exoplanets might have similar structures dominated by liquid
metallic hydrogen (LMH).
