Imaging black holes through AdS/CFT. (arXiv:1811.12617v1 [hep-th])
<a href="http://arxiv.org/find/hep-th/1/au:+Hashimoto_K/0/1/0/all/0/1">Koji Hashimoto</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Murata_K/0/1/0/all/0/1">Keiju Murata</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Kinoshita_S/0/1/0/all/0/1">Shunichiro Kinoshita</a>
Clarifying conditions for the existence of a gravitational picture for a
given quantum field theory (QFT) is one of the fundamental problems in the
AdS/CFT correspondence. We propose a direct way to demonstrate the existence of
the dual black holes: Imaging an Einstein ring. We consider a response function
of the thermal QFT on a two-dimensional sphere under a time-periodic localized
source. The dual gravity picture, if exists, is a black hole in an asymptotic
global AdS$_4$ and a bulk probe field with a localized source on the AdS
boundary. The response function corresponds to the asymptotic data of the bulk
field propagating in the black hole spacetime. We find a formula which converts
the response function to the image of the dual black hole: The view of the sky
of the AdS bulk from a point on the boundary. Using the formula, we demonstrate
that, for a thermal state dual to the Schwarzschild-AdS$_4$ spacetime, the
Einstein ring is constructed from the response function. The evaluated Einstein
radius is found to be determined by the total energy of the dual QFT.
Clarifying conditions for the existence of a gravitational picture for a
given quantum field theory (QFT) is one of the fundamental problems in the
AdS/CFT correspondence. We propose a direct way to demonstrate the existence of
the dual black holes: Imaging an Einstein ring. We consider a response function
of the thermal QFT on a two-dimensional sphere under a time-periodic localized
source. The dual gravity picture, if exists, is a black hole in an asymptotic
global AdS$_4$ and a bulk probe field with a localized source on the AdS
boundary. The response function corresponds to the asymptotic data of the bulk
field propagating in the black hole spacetime. We find a formula which converts
the response function to the image of the dual black hole: The view of the sky
of the AdS bulk from a point on the boundary. Using the formula, we demonstrate
that, for a thermal state dual to the Schwarzschild-AdS$_4$ spacetime, the
Einstein ring is constructed from the response function. The evaluated Einstein
radius is found to be determined by the total energy of the dual QFT.
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