Complexity and shock wave geometries

Stanford University

Indexed inarxivcrossref

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.

Citation impact

770
total citations
FWCI
35.25
Percentile
100%
References
35
Citations per year

Authors

2

Topics & keywords

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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Funding