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Observability of the innermost stable circular orbit in a near-extremal Kerr black hole

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 Added by Takahisa Igata
 Publication date 2019
  fields Physics
and research's language is English




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We consider the escape probability of a photon emitted from the innermost stable circular orbit (ISCO) of a rapidly rotating black hole. As an isotropically emitting light source on a circular orbit reduces its orbital radius, the escape probability of a photon emitted from it decreases monotonically. The escape probability evaluated at the ISCO also decreases monotonically as the black hole spin increases. When the dimensionless Kerr parameter $a$ is at the Thorne limit $a=0.998$, the escape probability from the ISCO is $58.8%$. In the extremal case $a=1$, even if the orbital radius of the light source is arbitrarily close to the ISCO radius, which coincides with the horizon radius, the escape probability remains at $54.6%$. We also show that such photons that have escaped from the vicinity of the horizon reach infinity with sufficient energy to be potentially observed because Doppler blueshift due to relativistic beaming can overcome the gravitational redshift. Our findings indicate that signs of the near-horizon physics of a rapidly rotating black hole will be detectable on the edge of its shadow.

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We compute the radiation emitted by a particle on the innermost stable circular orbit of a rapidly spinning black hole both (a) analytically, working to leading order in the deviation from extremality and (b) numerically, with a new high-precision Teukolsky code. We find excellent agreement between the two methods. We confirm previous estimates of the overall scaling of the power radiated, but show that there are also small oscillations all the way to extremality. Furthermore, we reveal an intricate mode-by-mode structure in the flux to infinity, with only certain modes having the dominant scaling. The scaling of each mode is controlled by its conformal weight, a quantity that arises naturally in the representation theory of the enhanced near-horizon symmetry group. We find relationships to previous work on particles orbiting in precisely extreme Kerr, including detailed agreement of quantities computed here with conformal field theory calculations performed in the context of the Kerr/CFT correspondence.
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