Exact derivation of the Hawking effect in canonical formulation

The Hawking effect is one of the most extensively studied topics in modern physics, yet it remains relatively underexplored within the framework of canonical quantization. The key difficulty lies in the fact that the Hawking effect is principally understood using the relation between the ingoing modes which leave past null infinity and the outgoing modes which arrive at future null infinity. Naturally, these modes are described using advanced and retarded null coordinates instead of the usual Schwarzschild coordinates. However, null coordinates do not lead to a true Hamiltonian that describes the evolution of these modes. In order to overcome these hurdles in a canonical formulation, we introduce here a set of near-null coordinates which allows one to perform an exact Hamiltonian-based derivation of the Hawking effect. This derivation opens up an avenue to explore the Hawking effect using different canonical quantization methods such as polymer quantization.