Probing the Black Hole Interior with Holographic Entanglement Entropy and the Role of AdS/BCFT Correspondence

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