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

• Published in: The journal of high energy physics Vol. 2021; no. 5; pp. 1 - 30
• Main Authors: Bhattacharya, Aranya, Bhattacharyya, Arpan, Nandy, Pratik, Patra, Ayan K.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2021; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Black Holes; Black Holes in String Theory; Branes; Classical and Quantum Gravitation; Complexity; Elementary Particles; High energy physics; Islands; Models of Quantum Gravity; Phase transitions; Physics; Physics and Astronomy; Quantum entanglement; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Radiation; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Subsystems; Black Holes in String Theory; AdS-CFT Correspondence; Black Holes; Models of Quantum Gravity
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2021)135

A bstract 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.