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P53: Ryu-Takayanagi Entropy and Page Curve in CCEGA Black Stars

Year: 2026
Type: conference-abstract
Abstract: The UV-anchored RT entropy estimate S_UV ~ 10^94 k_B (Section 3.2) assumed the minimal surface reaches the UV brane, requiring R_final > z_IR. P54 (doi:10.5281/zenodo.20349504) shows that for stellar-mass black stars R_final/z_IR = 0.21, invalidating this limit. Corrected values: S_RT ~ 5 × 10^53 k_B and t_Page ~ 10^59 yr. The island structure and all qualitative conclusions of Sections 6 and 8 are preserved. Only the quantitative entropy scale requires revision. The limitation was explicitly flagged in Section 7.1 of this paper. We compute the Ryu-Takayanagi (RT) entropy for CCEGA black stars in the RS1 AdS₅ bulk. Two competing extremal surfaces are identified. The ρ_c surface acts spontaneously as a Penington island. Page time estimated at t_Page ~ 5×10⁸³ yr, S_Page ~ 6×10⁷⁷ k_B. AdS curvature scale k ~ Λ_QCD ~ 200 MeV derived from the RS chain (exploratory). Note: RT entropy value corrected in P54. Correction added in v1.2 (May 2026): The RT entropy estimate of v1.0 (S_RT ~ 10^94 k_B) assumed the minimal Ryu-Takayanagi surface reaches the UV brane, which requires R_final > z_IR. P54 (doi:10.5281/zenodo.20349504) shows that for stellar-mass black stars (4.56–12.0 M☉), the correct ratio is R_final/z_IR = 0.21 < 1. The RT surface remains near the IR brane, penetrating the bulk by only 0.05%. Corrected value: S_RT ~ 5 × 10^53 k_B, a factor 10^25 below Bekenstein-Hawking. Corrected Page time: t_Page ~ 10^59 yr, not 10^83 yr. The Penington island structure is preserved qualitatively — the ρ_c surface remains an extremal surface. However, the quantitative estimates require revision. The UV-anchored regime (S_RT ~ S_BH) applies for M ≳ 10^3 M☉, relevant for Sgr A* and M87*.
DOI: 10.5281/zenodo.20335208
Language: English
Open Access status: green
OpenAlex ID: W7162113657
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