A new Kerr-like metric with quadrupole moment is obtained by means ofperturbing the Kerr spacetime. The form of this new metric is simple as theKerr metric. By comparison with the exterior Hartle-Thorne metric, it is shownthat it could be matched to an interior solution. This approximate metric mayrepresent the spacetime of a real astrophysical object with any Kerr rotationparameter a and slightly deformed.
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