Holographic Complexity Equals Bulk Action
TLDR
The hypothesis that black holes are the fastest computers in nature is discussed and the conjecture that the quantum complexity of a holographic state is dual to the action of a certain spacetime region that is called a Wheeler-DeWitt patch is illustrated.Abstract:
We conjecture that the quantum complexity of a holographic state is dual to the action of a certain spacetime region that we call a Wheeler-DeWitt patch. We illustrate and test the conjecture in the context of neutral, charged, and rotating black holes in anti-de Sitter spacetime, as well as black holes perturbed with static shells and with shock waves. This conjecture evolved from a previous conjecture that complexity is dual to spatial volume, but appears to be a major improvement over the original. In light of our results, we discuss the hypothesis that black holes are the fastest computers in nature.read more
Citations
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References
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Journal ArticleDOI
The world as a hologram
TL;DR: In this article, the effects of particle growth with momentum on information spreading near black hole horizons were investigated. But the authors only considered the earliest times of the propagation of information near the horizon.
Journal ArticleDOI
A bound on chaos
TL;DR: In this paper, a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom is given, based on plausible physical assumptions, establishing this conjecture.
Journal ArticleDOI
Black holes and the butterfly effect
TL;DR: In this article, the authors used holography to study sensitive dependence on initial conditions in strongly coupled field theories and showed that the effect of the early infalling quanta relative to the t = 0 slice creates a shock wave that destroys the local two-sided correlations present in the unperturbed state.
Journal ArticleDOI
The String landscape, black holes and gravity as the weakest force
TL;DR: In this paper, an upper bound on the strength of gravity relative to gauge forces in quantum gravity was given, motivated by arguments involving holography and absence of remnants, the stability of black holes as well as the non-existence of global symmetries in string theory.
Dimensional reduction in quantum gravity
TL;DR: In this article, Abdus Salam argued that the observable degrees of freedom can best be described as if they were Boolean variables defined on a two-dimensional lattice, evolving with time.