Aspects of entanglement entropy, the information paradox and physics-informed deep learning

Abstract

This thesis explores entanglement entropy, the black hole information paradox, and applications of physics-informed deep learning, with the Anti-de Sitter/conformal field theory (AdS/CFT) correspondence serving as a central framework.

The first part examines entanglement islands as a possible resolution to the information paradox. Islands are surfaces in spacetime that contribute to purifying Hawking radiation in semi-classical gravity. We derive the entanglement entropy for annular entangling regions on d-dimensional AdS black hole backgrounds, and show that islands are highly sensitive to the underlying field theory modeling radiation - not only in details but in their very existence. Furthermore, we show how inhomogeneous transformations of entanglement entropy, via the replica trick, encode details about island formation, reflected in the stress tensor on both replica and base manifolds. We also introduce a framework for computing replica corrections to the thermal stress tensor, with intrinsic interest. To make contact with islands in positively curved spacetimes, we construct a multiverse model using T2-deformed dS wedge holography with dS Jackiw–Teitelboim gravity on infrared end-of-the-world branes, where finite-cutoff observers recover Page curves via islands.

The second part investigates physics-informed neural networks (PINNs), which embed physical laws into the loss function. Motivated by the challenge of evaluating holographic entanglement entropy with sparse boundary data, we apply Bayesian PINNs (B-PINNs) to solve the corresponding nonlinear PDEs. The latter exemplifies high-energy theory complexities, extending PINNs beyond traditional engineering uses. We examine overconfidence in these models, attributing it to physical priors in the loss rather than miscalibration, and introduce diagnostic tools to assess this effect. Further, Hessian decomposition reveals how constraints hierarchically influence network behavior and shape the solution space, in a non-trivial way when varying with loss weight adjustments.

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Identifiers

ORCID for Kostas Skenderis: orcid.org/0000-0003-4509-5472

ORCID for Marika Taylor: orcid.org/0000-0001-9956-601X

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