Quasinormal Modes of Generalized Black Holes: delta-Kerr Spacetime

TL;DR

This paper investigates the quasinormal modes of a generalized black hole spacetime called delta-Kerr, which incorporates quadrupole deformations, and compares its QNM frequencies to those of known rotating solutions.

Contribution

It introduces the delta-Kerr spacetime as a deformed Kerr black hole with quadrupole moment and analytically computes its quasinormal mode frequencies using ray and wave methods.

Findings

QNM frequencies are similar to those of rotating Hartle-Thorne spacetime.

Outer singularity remains a null hypersurface for certain parameter ranges.

Analytical determination of QNM frequencies in the delta-Kerr spacetime.

Abstract

The nonlinear superposition of the delta-metric and the Kerr metric results in delta-Kerr metric that represents a deformed Kerr black hole with delta = 1 + q, where q > 0 is proportional to the nonrelativistic quadrupole moment of the collapsed configuration. We study this spacetime and determine q_{+} such that for q, 0 < q < q_{+}, the outer spacetime singularity remains a null hypersurface. In this case, delta-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 delta-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 delta-Kerr spacetime turn out to be nearly the same as those of the rotating Hartle-Thorne spacetime.