Quasinormal modes of generalized black holes: <i>δ</i> -Kerr spacetime

Abstract The nonlinear superposition of the -metric and the Kerr metric results in a -Kerr metric that represents a deformed Kerr black hole with , where q &gt; 0 is proportional to the nonrelativistic quadrupole moment of the collapsed configuration. We study this spacetime and determine q + such that for q , 0 &lt; q &lt; q + , the outer spacetime singularity remains a null hypersurface. In this case, -Kerr spacetime represents a generalized black hole, namely, an asymptotically flat, stationary and axisymmetric vacuum solution of general relativity for which the outer singularity is a closed null hypersurface. For an approximate variant of -Kerr spacetime characterized by mass M , quadrupole parameter q and angular momentum parameter a , where the latter two parameters are treated to first and second orders of approximation, respectively, we analytically determine the quasinormal mode (QNM) frequencies in the ray approach using the light-ring method as well as in the complementary wave approach for massless scalar field perturbations in the a = 0 limit. The QNM frequencies of -Kerr spacetime turn out to be nearly the same as those of the rotating Hartle–Thorne spacetime.

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