the atomic positions have not been determined
within its unit cell, and the small unit cell that we
provided could well be the base for larger super-lattices (20). Its composition and phase relation
to pv and ppv needs to be determined as a function of P-T for interpreting various features in
the deep lower mantle. Last, its elasticity and
rheological properties are essential for interpretation of deep Earth seismology.
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We thank Y. Fei for providing the pv10 starting material; J. Shu,
M. Somayazulu, E. Rod, G. Shen, S. Sinogeikin, P. Dera,
V. Prakapenka, and S. Tkachev for their technical support. We
also thank S. Merkel for introducing us to the indexing software.
The research is supported by National Science Foundation
(NSF) grants EAR-0911492, EAR-1119504, EAR-1141929, and
EAR-1345112. This work was performed at HPCAT (Sector 16),
Advanced Photon Source (APS), Argonne National Laboratory.
HPCAT operations are supported by the U.S. Department of
Energy–National Nuclear Security Administration (DOE-NNSA)
under award DE-NA0001974 and DOE–Basic Energy Sciences
(BES) under award DE-FG02-99ER45775, with partial
instrumentation funding by NSF. HPSynC is supported as part of
EFree, an Energy Frontier Research Center funded by DOE-BES
under grant DE-SC0001057. Portions of this work were performed
at GeoSoilEnviroCARS (sector 13), APS, supported by the
NSF-Earth Sciences (EAR-1128799) and DOE-GeoSciences
(DE-FG02-94ER14466), at 34ID-E beamline, APS, and at 15U1,
Shanghai Synchrotron Radiation Facility. Use of the APS facility
was supported by DOE-BES under contract DE-AC02-06CH11357.
This work was also partially supported by the Materials Research
and Engineering Center program of the NSF under award
DMR-0819885. Part of this work was carried out in the
Characterization Facility of the University of Minnesota. All other
data used to support conclusions in this manuscript are provided
in the supplementary materials
Materials and Methods
Figs. S1 to S11
Tables S1 and S2
30 December 2013; accepted 3 April 2014
Holographic description of a
quantum black hole on a computer
Masanori Hanada,1,2,3 Yoshifumi Hyakutake,4 Goro Ishiki,1 Jun Nishimura5,6
Black holes have been predicted to radiate particles and eventually evaporate,
which has led to the information loss paradox and implies that the fundamental laws
of quantum mechanics may be violated. Superstring theory, a consistent theory of
quantum gravity, provides a possible solution to the paradox if evaporating black
holes can actually be described in terms of standard quantum mechanical systems,
as conjectured from the theory. Here, we test this conjecture by calculating the
mass of a black hole in the corresponding quantum mechanical system numerically.
Our results agree well with the prediction from gravity theory, including the leading
quantum gravity correction. Our ability to simulate black holes offers the potential to
further explore the yet mysterious nature of quantum gravity through well-established
In 1974, it was realized that a black hole should radiate particles as a perfect black bodydueto quantumeffects inthesurround- ing space and that the black hole should eventually evaporate completely (1, 2). This
phenomenon, which is known as the Hawking
radiation, made more accurate the close analogy
between the laws of black hole physics and
those of thermodynamics (3), but it also caused
a long scientific debate (4, 5) concerning the
information-loss paradox (6, 7). Suppose one
throws a book into a black hole. While the
black hole evaporates, all we observe is the black-
body radiation. Therefore, the information con-
tained in the book is lost forever. This statement
sharply conflicts with a basic consequence of
the law of quantum mechanics that the informa-
tion of the initial state should never disappear.
Then the question is whether the law of quantum mechanics is violated or the above argument
should somehow be modified if full quantum
effects of gravity are taken into account.
Superstring theory, a consistent theory of
quantum gravity, enabled us to understand the
statistical-mechanical origin of the black hole
entropy for a special class of stable black holes
by counting the microscopic states, which look
like the same black hole from a distant observer
(8). The paradox still remains, however, because
a complete description of an evaporating black
hole is yet to be established. A key to resolve the
paradox is provided by the gauge-gravity duality
(9), which is conjectured in superstring theory.
In a particular case, it claims that black holes in
gravity theory can be described in terms of gauge
theory in one dimension, which is a standard
quantum mechanical system without gravity. The
conjecture may be viewed as a concrete realiza-tion of the holographic principle (10, 11), which
states that all of the information inside a black
hole should be somehow encoded on its boundary, namely on the so-called event horizon of the
black hole. In gauge theory in general, information is conserved during the time evolution as
the standard laws of quantum mechanics simply
apply. Therefore, it is widely believed that there
is no information loss if the conjectured holographic description of a black hole is correct,
including full quantum effects of gravity.
1Yukawa Institute for Theoretical Physics, Kyoto University,
Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan.
2The Hakubi Center for Advanced Research, Kyoto
University, Yoshida Ushinomiyacho, Sakyo-ku, Kyoto
606-8501, Japan. 3Stanford Institute for Theoretical Physics,
Stanford University, Stanford, CA 94305, USA. 4College of
Science, Ibaraki University, Bunkyo 2-1-1, Mito, Ibaraki
310-8512, Japan. 5Theory Center, High Energy Accelerator
Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki
305-0801, Japan. 6Graduate University for Advanced Studies
(SOKENDAI), 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan.
*Corresponding author. E-mail: email@example.com