Abstract
A new approximate metric representing the spacetime of a rotating deformed body is obtained by perturbing the Kerr metric to include up to the second order of the quadrupole moment. It has a simple form, because it is Kerr-like. Its Taylor expansion form coincides with second order quadrupole metrics with slow rotation already found. Moreover, it can be transformed to an improved Hartle-Thorne metric, which guarantees its validity to be useful in studying compact object, and it is possible to find an inner solution.
Highlights
Nowadays, it is widely believed that the Kerr metric does not represent the spacetime of a rotating astrophysical object
We develop a perturbative method by means of the Lewis metric [5] to find solutions with quadrupole moment, using the Kerr spacetime as seed metric
It is shown that the application of this method leads to a new approximate solution to the Einstein field equations (EFE) with rotation and quadrupole moment. It is checked by means of a REDUCE program that the resulting metric is a solution of the EFE [15], and this program is available upon request
Summary
It is widely believed that the Kerr metric does not represent the spacetime of a rotating astrophysical object. The Ernst formalism [3] and the Hoenselaers-Kinnersley-Xanthopoulos (HKX) transformations [4] are very useful to find exact axial solutions of the Einstein field equations (EFE) These formalisms allow to include desirable characteristics (rotation, multipole moments, magnetic dipole, etc.) to a given seed metrics. It is checked by means of a REDUCE program that the resulting metric is a solution of the EFE [15], and this program is available upon request.
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