articlePhysical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmologyDec 11, 2014GREEN OA
Complexity and shock wave geometries
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Abstract
In this paper we refine a conjecture relating the time-dependent size of an Einstein-Rosen bridge (ERB) to the computational complexity of the dual quantum state. Our refinement states that the complexity is proportional to the spatial volume of the ERB. More precisely, up to an ambiguous numerical coefficient, we propose that the complexity is the regularized volume of the largest codimension one surface crossing the bridge, divided by ${G}_{N}{l}_{\mathrm{AdS}}$. We test this conjecture against a wide variety of spherically symmetric shock wave geometries in different dimensions. We find detailed agreement.
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Authors
2Topics & keywords
Topics
Keywords
- Conjecture
- Bridge (graph theory)
- Variety (cybernetics)
- Computational complexity theory
- Shock wave
- Quantum
- Shock (circulatory)
- Einstein
UN Sustainable Development Goals
- Sustainable cities and communities
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