Approximate Metric for a Rotating Deformed Mass
  A new Kerr-like metric with quadrupole moment is obtained by means of perturbing the Kerr spacetime. The form of this new metric is simple as the Kerr metric. By comparison with the exterior Hartle-Thorne metric, it is shown that it could be matched to an interior solution. This approximate metric may represent the spacetime of a real astrophysical object with any Kerr rotation parameter a and slightly deformed. 
Francisco Frutos-Alfaro, Paulo Montero-Camacho, Miguel Araya-Arguedas,   Javier Bonatti-Gonzalez
astro-ph.CO gr-qc