Observer Dependent Horizon Temperatures: a Coordinate-Free Formulation of Hawking Radiation as Tunneling

Understand

We reformulate the Hamilton-Jacobi tunneling method for calculating Hawking radiation in static, spherically-symmetric spacetimes by explicitly incorporating a preferred family of frames.

• These frames correspond to a family of observers tied to a locally static timelike Killing vector of the spacetime.
• This formulation separates the role of the coordinates from the choice of vacuum and thus provides a coordinate-independent formulation of the tunneling method.
• In addition, it clarifies the nature of certain constants and their relation to these preferred observers in the calculation of horizon temperatures.