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<p>The island paradigm for an AdS<sub>2</sub> 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 <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="double-struck">U</mi> <mtext>bath</mtext> </msub> </math></EquationSource> <EquationSource Format="TEX">\( {\mathbbm{U}}_{\textrm{bath}} \)</EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="double-struck">U</mi> <mtext>bath</mtext> </msub> </math></EquationSource> <EquationSource Format="TEX">\( {\mathbbm{U}}_{\textrm{bath}} \)</EquationSource> </InlineEquation> 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.</p>

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Island paradigm and information recovery from radiation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月24日

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  • Krishna Jalan,
  • Roji Pius,
  • Manish Ramchander

摘要

The island paradigm for an AdS2 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 U bath \( {\mathbbm{U}}_{\textrm{bath}} \) 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 U bath \( {\mathbbm{U}}_{\textrm{bath}} \) 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.