  An approximate realistic metric representing the spacetime of neutron stars
is obtained by perturbing the Kerr metric. This metric has five parameters,
namely the mass, spin or angular momentum, mass quadrupole, spin octupole and
mass hexadecapole. Moreover, a version of the Hartle-Thorne metric containing
these parameters is constructed by means of a series transformation between
these spacetimes and solving the Einstein field equations. The form of the
Pappas metric in Schwarzschild spherical coordinates is found. The three
relativistic multipole structures are compared.
