A recent publication revealed unexpected observations about dark matter. In particular, the observed baryonic mass should probably be sufficient to explain the observed rotation curves (i.e. without dark matter) and their observations gave an empirical relation for weak accelerations. This present work demonstrated that the equations of general relativity allow explaining the term of dark matter (without new matter) in agreement with the results of this publication and allow retrieving this empirical relation (observed values and characteristics of this correlation's curve). These observations constrain drastically the possible gravitational potential in the frame of general relativity to explain the term of dark matter. This theoretical solution has already been studied with several unexpected predictions that have recently been observed. For example, an article revealed that early galaxies (ten billion years ago) didn't have dark matter and a more recent paper showed unlikely alignments of galaxies. To finish the main prediction of this solution, it is recalled: the term of dark matter should be a Lense-Thirring effect, around the earth, of around 0.3 and 0.6 milliarcsecond/year.