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Abstract

This work explores the black hole information loss paradox, a fundamental challenge in theoretical physics. It proposes insights using Holographic Entanglement Entropy (HEE) and the AdS/BCFT correspondence within Horndeski gravity. The work revisits the time-dependent behavior of HEE to probe black hole interiors and examines its implications for the Page curve, which describes the entropy evolution of Hawking radiation. It also discusses the relationship between conformal field theory (CFT) microstates and black hole thermodynamics through the AdS/BCFT correspondence, suggesting that only a subset of microstates corresponds to black holes with smooth interiors, while others may involve firewalls. The study extends black hole thermal entropy to time-dependent entanglement entropy, offering a perspective on the interplay between quantum mechanics, thermodynamics, and gravity.