General relativity and quantum mechanics are the twin pillars of modern physics, yet their unification remains one of the deepest open problems in science. This volume explores the fertile territory where these frameworks meet, the semiclassical frontier, asking what can be reliably calculated when quantum fields propagate on curved spacetime and when gravity affects quantum systems.

The contributions survey quantum field theory in curved spacetime, black hole thermodynamics, and the black hole information paradox, including recent work on entanglement islands and Page curves. They analyze gravitational phase shifts in matter-wave interferometry, quantum effects in realistic black hole environments, and the role of entropy and entanglement in semiclassical gravity. The book also reviews theoretical extensions such as extra-dimensional models of the hierarchy problem and supersymmetric systems that illuminate vacuum energy cancellations and the structure of quantum spectra.

A recurring theme is that entropy and entanglement appear across seemingly disparate contexts, including Hawking radiation, quantum extremal surfaces, interferometry, and supersymmetric toy models, suggesting that these concepts lie at the heart of any future theory of quantum gravity. Throughout, the chapters emphasize explicit, worked calculations such as phase-shift formulas, entropy prescriptions, and partition functions that readers can follow, modify, and apply in their own research.

Aimed at advanced students and researchers, this volume offers a rigorous, self-contained overview of current tools at the quantum–gravity interface. It does not claim a final theory, but it does provide a clear map of the questions that can now be posed precisely, the methods available to address them, and the experimental and observational arenas, from atom interferometry to black hole imaging, where semiclassical ideas can be tested.