The EGUP-Induced Critical Radius: A New Holographic Scale for Quantum Gravity

arXiv:2511.20777v1 Announce Type: new
Abstract: We present a unified framework incorporating both the Generalized and Extended Uncertainty Principles (GUP/EUP) in Anti-de Sitter space. This reveals a fundamental quantum gravity scale, the textit{critical radius} $r_{rm crit}=(beta/gamma)^{1/4}sqrt{ell_{P}L}$, which marks a phase transition where quantum gravitational ($beta$) and AdS curvature ($gamma$) effects equilibrate. At this scale, we demonstrate three interconnected phenomena: (i) a breakdown of the standard holographic duality, signaled by the exact vanishing of the boundary stress tensor $langle T_{munu}rangle=0$ under the self-duality condition $partial_z g_{munu}|_{z=r_{rm crit}}=0$; (ii) a topological transition manifested by the complexification of the central charge, $c_{rm eff}=cleft(1+frac{i}{2}sqrt{kappa}ell_{P}^{2}right)$ with $kappa=(beta/gamma)^{1/4}sqrt{betagammaell_P/L}$; and (iii) a mechanism as a scenario for information paradox resolution, where information is recovered via topological storage in Chern-Simons states, modifying the Page curve with $Delta S_{rm recovery}>0$. These effects establish a consistency condition $L>sqrt{beta}ell_{P}$ for a valid AdS/CFT correspondence and identify $r_{rm crit}$ as the thermodynamic critical point where black holes transition to stringy remnants and information is topologically scrambled.