Holographic Complexity and Thermodynamic Volume.

Abdulrahim Al Balushi,Robie A Hennigar,Robert B Mann,Hari K Kunduri

doi:10.1103/physrevlett.126.101601

Abdulrahim Al Balushi, Robie A Hennigar + Show 2 more

Open Access

https://doi.org/10.1103/physrevlett.126.101601

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Abstract

We study the holographic complexity conjectures for rotating black holes, uncovering a relationship between the complexity of formation and the thermodynamic volume of the black hole. We suggest that it is the thermodynamic volume and not the entropy that controls the complexity of formation of large black holes in both the complexity equals action and complexity equals volume proposals in general. Our proposal reduces to known results involving the entropy in settings where the thermodynamic volume and entropy are not independent, but has broader scope. Assuming a conjectured inequality is obeyed by the thermodynamic volume, we establish that the complexity of formation is bounded from below by the entropy for large black holes.

Highlights

In recent years there has been dramatic progress in understanding the connections between gravity and quantum information
Assuming a conjectured inequality is obeyed by the thermodynamic volume, we establish that the complexity of formation is bounded from below by the entropy for large black holes
Through the Ryu-Takayanagi prescription and its generalizations [1,2,3,4] the duality relates entanglement between spacetime regions in the field theory to the existence of minimal surfaces in the bulk, a situation often described by the slogan “entanglement 1⁄4 geometry.”

Summary

Holographic Complexity and Thermodynamic Volume

We study the holographic complexity conjectures for rotating black holes, uncovering a relationship between the complexity of formation and the thermodynamic volume of the black hole. A number of properties of complexity as defined by the CV and CA proposals are well-understood for black holes, with both proposals generally yielding qualitatively similar results, but not always [13,14,15,16,17,18,19,20] In both proposals it is known that at late times the complexity grows linearly in time at a rate characterized by the mass, or other thermodynamic potentials, of the black hole [11,21,22,23,24].

Published by the American Physical Society

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