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arXiv · 1710.06415

Holographic non-computers

Jose L. F. Barbon·Javier Martin-Garcia
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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.

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Jose L. F. Barbon, Javier Martin-Garcia. 2017-10-17. Holographic non-computers. https://doi.org/10.1007/jhep02(2018)181

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