Island Paradigm and Information Recovery from Radiation

Abstract

The island paradigm for an AdS${}_2$ eternal black hole in the Hartle-Hawking state coupled to a finite temperature non-gravitating bath asserts that after the Page time the operators in the black hole interior can be reconstructed using the bath degrees of freedom. We demonstrate this assertion by consideing a special operator ${\mathbb{U}}_{bath}$ that has nontrivial action only on the bath degrees of freedom. We show via the gravitational Euclidean path integral analysis that though before the Page time ${\mathbb{U}}_{bath}$ does not translate the operators in the bath to the black hole interior, after the Page time it takes them to the black hole interior.

Version accepted for publication in JHEP, 27 pages, 12 figures