  Approximate all-terrain spacetimes for astrophysical applications are
presented. The metrics possess five relativistic multipole moments, namely
mass, rotation, mass quadrupole, charge, and magnetic dipole moment. All these
spacetimes approximately satisfy the Einstein-Maxwell field equations. The
first metric is generated by means of the Hoenselaers-Perj\'es method from
given relativistic multipoles. The second metric is a perturbation of the
Kerr-Newman metric, which makes it a relevant approximation for astrophysical
calculations. The last metric is an extension of the Hartle-Thorne metric that
is important for obtaining internal models of compact objects perturbatively.
The electromagnetic field is calculated using Cartan forms for locally
nonrotating observers. These spacetimes are relevant to infer properties of
compact objects from astrophysical observations. Furthermore, the numerical
implementations of these metrics are straightforward, making them versatile for
simulating the potential astrophysical applications.
