The MSA system of coordinates [1] for the M Q-solution [2] is proved to be
the unique solution of certain partial differential equation with boundary and
asymptotic conditions. Such a differential equation is derived from the
orthogonality condition between two surfaces which hold a functional
relationship. The obtained expressions for the MSA system recover the
asymptotic expansions previously calculated [1] for those coordinates, as well
as the Erez-Rosen coordinates in the spherical case. It is also shown that the
event horizon of the M Q-solution can be easily obtained from those coordinates
leading to already known results. But in addition, it allows us to correct a
mistaken conclusion related to some bound imposed to the value of the
quadrupole moment [3]. Finally, it is explored the possibility of extending
this method of generalizing the Erez-Rosen coordinates to the general case of
solutions with any finite number of Relativistic Multipole Moments (RMM). It is
discussed as well, the possibility of determining the Weyl moments of those
solutions from their corresponding MSA coordinates, aiming to establish a
relation between the uniqueness of the MSA coordinates and the solutions
itself.Comment: Accepted to be published in Classical and Quantum Gravity, May 201
