Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model

Aranya Bhattacharya, Arpan Bhattacharyya, Pratik Nandy, Ayan K. Patra

TL;DR

This work analyzes entanglement islands and subregion volume complexity in a doubly holographic Randall-Sundrum setup, modeling the defect’s left (gravitating) and right (bath) sectors as an eternal black hole and its radiation. By computing volumes dual to HM and island RT surfaces on both branes, the authors show a Page-time transition where island surfaces dominate, causing a jump in the left-brane complexity and a corresponding, growing jump in the right-brane (radiation) complexity. The results reveal a consistent qualitative picture with covariant complexity proposals and highlight the role of brane angles and spacetime dimensionality in governing Page-time dynamics. The findings point toward a universal feature of complexity evolution in island-augmented holography and motivate further field-theoretic investigations and covariant refinements.

Abstract

We study the entanglement islands and subsystem volume complexity corresponding to the left/ right entanglement of a conformal defect in $d$-dimensions in Randall-Sundrum (RS) braneworld model with subcritical tension brane. The left and right modes of the defect mimic the eternal black hole and radiation system respectively. Hence the entanglement entropy between the two follows an eternal black hole Page curve which is unitarity compatible. We compute the volumes corresponding to the left and right branes with preferred Ryu-Takanayagi (RT) surfaces at different times, which provide a probe of the subregion complexity of the black hole and the radiation states respectively. An interesting jump in volume is found at Page time, where the entanglement curve is saturated due to the inclusion of the island surfaces. We explain various possibilities of this phase transition in complexity at Page time and argue how these results match with a covariant proposal qualitatively.

Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model

TL;DR

This work analyzes entanglement islands and subregion volume complexity in a doubly holographic Randall-Sundrum setup, modeling the defect’s left (gravitating) and right (bath) sectors as an eternal black hole and its radiation. By computing volumes dual to HM and island RT surfaces on both branes, the authors show a Page-time transition where island surfaces dominate, causing a jump in the left-brane complexity and a corresponding, growing jump in the right-brane (radiation) complexity. The results reveal a consistent qualitative picture with covariant complexity proposals and highlight the role of brane angles and spacetime dimensionality in governing Page-time dynamics. The findings point toward a universal feature of complexity evolution in island-augmented holography and motivate further field-theoretic investigations and covariant refinements.

Abstract

We study the entanglement islands and subsystem volume complexity corresponding to the left/ right entanglement of a conformal defect in -dimensions in Randall-Sundrum (RS) braneworld model with subcritical tension brane. The left and right modes of the defect mimic the eternal black hole and radiation system respectively. Hence the entanglement entropy between the two follows an eternal black hole Page curve which is unitarity compatible. We compute the volumes corresponding to the left and right branes with preferred Ryu-Takanayagi (RT) surfaces at different times, which provide a probe of the subregion complexity of the black hole and the radiation states respectively. An interesting jump in volume is found at Page time, where the entanglement curve is saturated due to the inclusion of the island surfaces. We explain various possibilities of this phase transition in complexity at Page time and argue how these results match with a covariant proposal qualitatively.

Paper Structure

This paper contains 19 sections, 25 equations, 11 figures.

Table of Contents

  1. Introduction:
  2. Review of Left/Right Entanglement in RS brane model:
  3. Hartman-Maldacena and Island Areas: Revisited
  4. Hartman-Maldacena Area:
  5. Island Area:
  6. Critical Anchor at $d=4$ and $d=3$:
  7. Volume Subregion Complexity:
  8. Volumes Corresponding to Left Brane (Eternal Black Hole):
  9. Hartman-Maldacena Volume:
  10. Volume after Page time:
  11. General Discussion on Left Brane Volumes:
  12. Volumes Corresponding to Right Brane (Radiation):
  13. Hartman-Maldacena Volume:
  14. Island Volume:
  15. General Discussion on Right Brane Volume:
  16. ...and 4 more sections

Figures (11)

  • Figure 1: The braneworld model and the preferred RT surfaces before (HM surface) and after (island surface) Page time.
  • Figure 2: Page curves for $d=4$ and $d=3$.
  • Figure 3: Critical anchor at $d=4$ for different values of physical (left) brane angle.
  • Figure 4: Critical anchor at $d=3$ for different values of physical (left) brane angle.
  • Figure 5: Left (physical/gravitating) brane volumes before and after the Page time are shown. Before Page time, HM surface $u=u(t)$ is the RT surface whereas after Page time, the preferred RT surface is the Island surface $u(\mu)$ specified by the critical anchor. Correspondingly volumes on the left brane become (\ref{['figHMvol']}) before Page time and (\ref{['figislandvol']}) after page time.
  • ...and 6 more figures