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Researchers explored entangled black hole states, revealing they contain complex wormholes. A new relation links quantum randomness to wormhole geometry, suggesting "complexity = geometry".

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Area of Science:

  • Theoretical physics
  • Quantum gravity
  • Black hole physics

Background:

  • Understanding the nature of entangled black hole states is crucial for quantum gravity.
  • Investigating the internal structure of black holes, particularly semiclassical interiors, remains a key challenge.

Purpose of the Study:

  • To characterize the typical entangled states of two-black-hole systems.
  • To determine if these states possess semiclassical interiors.
  • To explore the relationship between quantum information and black hole geometry.

Main Methods:

  • Constructing ensembles of states that densely sample the black hole Hilbert space.
  • Analyzing the structure of these states, identifying features like Einstein-Rosen caterpillars (wormholes with matter inhomogeneities).
  • Quantifying the distinction between these ensembles and typical entangled states.

Main Results:

  • The typical entangled states of two black holes contain very long Einstein-Rosen caterpillars.
  • These wormholes exhibit significant matter inhomogeneities.
  • A correspondence was derived between microscopic quantum randomness and the geometric length of the wormhole.

Conclusions:

  • The study provides a constructive approach to understanding entangled black hole states and their semiclassical interiors.
  • The findings formalize a "complexity = geometry" relation, linking quantum complexity to geometric properties of wormholes.
  • This work offers insights into the holographic principle and the nature of spacetime at the quantum level.