Quantum Fields in Curved Spacetime

Outline the canonical quantization of a scalar field in Minkowski spacetime, defining creation and annihilation operators.

Explain the ambiguity in defining particles in a general curved spacetime due to the lack of a global timelike Killing vector.

Define Bogoliubov transformations relating different sets of creation/annihilation operators.

Derive the Unruh effect: the thermal particle spectrum observed by a uniformly accelerating observer in Minkowski vacuum.

Formulate quantum field theory near a black hole's event horizon.

Derive the Hawking temperature of a Schwarzschild black hole by analyzing the Bogoliubov transformation between past and future null infinity.

Relate Hawking radiation to black hole thermodynamics, identifying the Bekenstein-Hawking entropy.

Discuss the black hole information paradox and its implications for quantum mechanics.