To the external observer, the black hole is perfectly spherically symmetrical.¹ The center of mass of a spherically symmetrical object is always right in the ce

To the external observer, the black hole is perfectly spherically symmetrical.¹ The center of mass of a spherically symmetrical object is always right in the center. Right where the singularity would be, if it weren’t for the fact that to the inside observer the singularity is now in the future at the end of time.² These types of coordinate changes are one reason why the subject is considered so hard. ¹ Except very briefly as two black holes merge. Or in the case of a rotating black hole. Or potentially during the formation of the black hole. But those are all complications and the subject is difficult enough. ² Except for the fact that the singularity might not actually exist if the interior of the black hole is growing without bound in the timelike direction. See ER=EPR.