Abstract
We introduce the notion of holographic non-computer as a system which exhibits parametrically large delays in the growth of complexity, as calculated within the Complexity-Action proposal. Some known examples of this behavior include extremal black holes and near-extremal hyperbolic black holes. Generic black holes in higher-dimensional gravity also show non-computing features. Within the 1/d expansion of General Relativity, we show that large-d scalings which capture the qualitative features of complexity, such as a linear growth regime and a plateau at exponentially long times, also exhibit an initial computational delay proportional to d. While consistent for large AdS black holes, the required ‘non-computing’ scalings are incompatible with thermodynamic stability for Schwarzschild black holes, unless they are tightly caged.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Susskind, Entanglement is not enough, Fortsch. Phys. 64 (2016) 49 [arXiv:1411.0690] [INSPIRE].
A.R. Brownet al., Complexity, action and black holes, Phys. Rev. D 93 (2016) 086006 [arXiv:1512.04993] [INSPIRE].
L. Susskind, Computational complexity and black hole horizons, Fortsch. Phys. 64 (2016) 44 [arXiv:1403.5695] [INSPIRE].
D. Stanford and L. Susskind, Complexity and shock wave geometries, Phys. Rev. D 90 (2014) 126007 [arXiv:1406.2678] [INSPIRE].
A.R. Brown, D.A. Roberts, L. Susskind, B. Swingle and Y. Zhao, Holographic complexity equals bulk action?, Phys. Rev. Lett. 116 (2016) 191301 [arXiv:1509.07876] [INSPIRE].
A.R. Brown and L. Susskind, The second law of quantum complexity, arXiv:1701.01107 [INSPIRE].
J. Álvarez and C. Gómez, A comment on fisher information and quantum algorithms, quant-ph/9910115.
L. Susskind, The typical-state paradox: diagnosing horizons with complexity, Fortsch. Phys. 64 (2016) 84 [arXiv:1507.02287] [INSPIRE].
S. Chapman, H. Marrochio and R.C. Myers, Complexity of formation in holography, JHEP 01 (2017) 062 [arXiv:1610.08063] [INSPIRE].
R. Emparan, R. Suzuki and K. Tanabe, The large D limit of general relativity, JHEP 06 (2013) 009 [arXiv:1302.6382] [INSPIRE].
S. Bhattacharyya, A. De, S. Minwalla, R. Mohan and A. Saha, A membrane paradigm at large D, JHEP 04 (2016) 076 [arXiv:1504.06613] [INSPIRE].
R.-G. Cai, S.-M. Ruan, S.-J. Wang, R.-Q. Yang and R.-H. Peng, Action growth for AdS black holes, JHEP 09 (2016) 161 [arXiv:1606.08307] [INSPIRE].
L. Lehner, R.C. Myers, E. Poisson and R.D. Sorkin, Gravitational action with null boundaries, Phys. Rev. D 94 (2016) 084046 [arXiv:1609.00207] [INSPIRE].
R. Emparan, AdS/CFT duals of topological black holes and the entropy of zero energy states, JHEP 06 (1999) 036 [hep-th/9906040] [INSPIRE].
J.L.F. Barbon and J. Martin-Garcia, Holographic complexity of cold hyperbolic black holes, JHEP 11 (2015) 181 [arXiv:1510.00349] [INSPIRE].
J.L.F. Barbon and J. Martinez-Magan, Spontaneous fragmentation of topological black holes, JHEP 08 (2010) 031 [arXiv:1005.4439] [INSPIRE].
R.-Q. Yang, C. Niu, C.-Y. Zhang and K.-Y. Kim, Comparison of holographic and field theoretic complexities for time dependent thermofield double states, JHEP 02 (2018) 082 [arXiv:1710.00600] [INSPIRE].
D. Carmi, S. Chapman, H. Marrochio, R.C. Myers and S. Sugishita, On the time dependence of holographic complexity, JHEP 11 (2017) 188 [arXiv:1709.10184] [INSPIRE].
L. Fidkowski, V. Hubeny, M. Kleban and S. Shenker, The black hole singularity in AdS/CFT, JHEP 02 (2004) 014 [hep-th/0306170] [INSPIRE].
S. Hod, Bulk emission by higher-dimensional black holes: almost perfect blackbody radiation, Class. Quant. Grav. 28 (2011) 105016 [arXiv:1107.0797] [INSPIRE].
S.W. Hawking and D.N. Page, Thermodynamics of black holes in Anti-de Sitter space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].
G.W. Gibbons and M.J. Perry, Black holes in thermal equilibrium, Phys. Rev. Lett. 36 (1976) 985 [INSPIRE].
B.F. Whiting and J.W. York Jr., Action principle and partition function for the gravitational field in black hole topologies, Phys. Rev. Lett. 61 (1988) 1336 [INSPIRE].
J.D. Brown and J.W. York Jr., Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D 47 (1993) 1407 [gr-qc/9209012] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black holes: complementarity or firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1710.06415
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Barbón, J.L.F., Martín-García, J. Holographic non-computers. J. High Energ. Phys. 2018, 181 (2018). https://doi.org/10.1007/JHEP02(2018)181
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2018)181