Quasinormal Modes of a Black Hole with Quadrupole Moment. (arXiv:1812.03376v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Allahyari_A/0/1/0/all/0/1">Alireza Allahyari</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Firouzjahi_H/0/1/0/all/0/1">Hassan Firouzjahi</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Mashhoon_B/0/1/0/all/0/1">Bahram Mashhoon</a>
We analytically determine the quasinormal mode (QNM) frequencies of a black
hole with quadrupole moment in the eikonal limit using the light-ring method.
The generalized black holes that are discussed in this work possess arbitrary
quadrupole and higher mass moments in addition to mass and angular momentum. In
particular, the generalized black hole that we consider for our extensive
calculations is a completely collapsed configuration whose exterior
gravitational field can be described by the Hartle-Thorne spacetime [Astrophys.
J. 153, 807-834 (1968)]. This collapsed system as well as its QNMs is
characterized by mass $M$, quadrupole moment $Q$ and angular momentum $J$,
where the latter two parameters are treated to first and second orders of
approximation, respectively. When the quadrupole moment is set equal to the
relativistic quadrupole moment of the corresponding Kerr black hole,
$J^2/(Mc^2)$, the Hartle-Thorne QNMs reduce to those of the Kerr black hole to
second order in angular momentum $J$. Using ringdown frequencies, one cannot
observationally distinguish a generalized Hartle-Thorne black hole with
arbitrary quadrupole moment from a Kerr black hole provided the dimensionless
parameter given by $|QMc^2-J^2|c^2/(G^2M^4)$ is sufficiently small compared to
unity.
We analytically determine the quasinormal mode (QNM) frequencies of a black
hole with quadrupole moment in the eikonal limit using the light-ring method.
The generalized black holes that are discussed in this work possess arbitrary
quadrupole and higher mass moments in addition to mass and angular momentum. In
particular, the generalized black hole that we consider for our extensive
calculations is a completely collapsed configuration whose exterior
gravitational field can be described by the Hartle-Thorne spacetime [Astrophys.
J. 153, 807-834 (1968)]. This collapsed system as well as its QNMs is
characterized by mass $M$, quadrupole moment $Q$ and angular momentum $J$,
where the latter two parameters are treated to first and second orders of
approximation, respectively. When the quadrupole moment is set equal to the
relativistic quadrupole moment of the corresponding Kerr black hole,
$J^2/(Mc^2)$, the Hartle-Thorne QNMs reduce to those of the Kerr black hole to
second order in angular momentum $J$. Using ringdown frequencies, one cannot
observationally distinguish a generalized Hartle-Thorne black hole with
arbitrary quadrupole moment from a Kerr black hole provided the dimensionless
parameter given by $|QMc^2-J^2|c^2/(G^2M^4)$ is sufficiently small compared to
unity.
http://arxiv.org/icons/sfx.gif
