Shadow and Quasinormal Modes of a Rotating Loop Quantum Black Hole. (arXiv:2003.00477v3 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Liu_C/0/1/0/all/0/1">Cheng Liu</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Zhu_T/0/1/0/all/0/1">Tao Zhu</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Wu_Q/0/1/0/all/0/1">Qiang Wu</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Jusufi_K/0/1/0/all/0/1">Kimet Jusufi</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Jamil_M/0/1/0/all/0/1">Mubasher Jamil</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Azreg_Ainou_M/0/1/0/all/0/1">Mustapha Azreg-Aïnou</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Wang_A/0/1/0/all/0/1">Anzhong Wang</a>
In this paper, we construct an effective rotating loop quantum black hole
(LQBH) solution, starting from the spherical symmetric LQBH by applying the
Newman-Janis algorithm modified by Azreg-A”{i}nou’s non-complexification
procedure, and study the effects of loop quantum gravity { (LQG) on its
shadow}. Given the rotating {LQBH}, we discuss its horizon, ergosurface, and
regularity {as} $r to 0$. Depending on the values of the specific angular
momentum $a$ and the polymeric function $P$ arising from {LQG}, we {find} that
the rotating solution we obtained can represent a regular black hole, a regular
extreme black hole, or a regular spacetime {without horizon (a non-black-hole
solution)}. We also {study} the effects of {LQG} and rotation, and {show} that,
in addition to the specific angular momentum, the polymeric function {also}
causes deformations in the size and shape of the black hole shadow.
Interestingly, for a given value of $a$ and inclination angle $theta_0$, the
apparent size of the shadow monotonically decreases, and the shadow gets more
distorted with increasing $P$. We also {consider the effects of $P$ on the
deviations from the circularity of the shadow, and find} that the deviation
from circularity increases with increasing $P$ for fixed values of $a$ and
$theta_0$. Additionally, we explore the observational implications of $P$ in
comparison with the latest Event Horizon Telescope (EHT) observation of the
supermassive black hole, M$87$. The connection between the shadow radius and
quasinormal modes in the eikonal limit as well as {the} deflection of massive
particles are also considered.
In this paper, we construct an effective rotating loop quantum black hole
(LQBH) solution, starting from the spherical symmetric LQBH by applying the
Newman-Janis algorithm modified by Azreg-A”{i}nou’s non-complexification
procedure, and study the effects of loop quantum gravity { (LQG) on its
shadow}. Given the rotating {LQBH}, we discuss its horizon, ergosurface, and
regularity {as} $r to 0$. Depending on the values of the specific angular
momentum $a$ and the polymeric function $P$ arising from {LQG}, we {find} that
the rotating solution we obtained can represent a regular black hole, a regular
extreme black hole, or a regular spacetime {without horizon (a non-black-hole
solution)}. We also {study} the effects of {LQG} and rotation, and {show} that,
in addition to the specific angular momentum, the polymeric function {also}
causes deformations in the size and shape of the black hole shadow.
Interestingly, for a given value of $a$ and inclination angle $theta_0$, the
apparent size of the shadow monotonically decreases, and the shadow gets more
distorted with increasing $P$. We also {consider the effects of $P$ on the
deviations from the circularity of the shadow, and find} that the deviation
from circularity increases with increasing $P$ for fixed values of $a$ and
$theta_0$. Additionally, we explore the observational implications of $P$ in
comparison with the latest Event Horizon Telescope (EHT) observation of the
supermassive black hole, M$87$. The connection between the shadow radius and
quasinormal modes in the eikonal limit as well as {the} deflection of massive
particles are also considered.
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