# New coordinates for a simpler canonical derivation of the Hawking effect

## TL;DR

This paper introduces a new coordinate system enabling a straightforward Hamiltonian-based derivation of the Hawking effect, overcoming previous challenges related to spacetime foliation and matter Hamiltonian formulation.

## Contribution

The authors propose novel coordinates that facilitate an exact canonical derivation of Hawking radiation without involving matter diffeomorphism generators.

## Key findings

- New coordinates enable canonical derivation of Hawking effect
- Avoids issues with non-spacelike hypersurfaces and matter Hamiltonian
- Simplifies the Hamiltonian approach to black hole radiation

## Abstract

In order to achieve a Hamiltonian-based canonical derivation of the Hawking effect, one usually faces multiple hurdles. Firstly, the spacetime foliation using Schwarzschild time does not lead to hyper-surfaces which are always spacelike. Secondly, the null coordinates which are frequently used in covariant approach, do not lead to a true matter Hamiltonian. Recently, an exact canonical derivation was presented using the so-called near-null coordinates. However, there too one faces the difficulty of having to deal with non-vanishing matter diffeomorphism generator as the spatial decomposition involves a non-zero shift vector. Here we introduce a new set of coordinates which allows one to perform an exact canonical derivation of Hawking effect without having to deal with matter diffeomorphism generator.