# Hawking radiation, quantum fields, and tunneling

## TL;DR

This paper examines the connection between tunneling models and quantum field theory in curved spacetime for black-hole radiation, revealing that the tunneling approach may be better understood as a WKB approximation to two-point functions rather than a direct tunneling process.

## Contribution

It clarifies the relationship between tunneling methods and quantum field theory, showing that the simplest tunneling approach corresponds to a WKB approximation rather than actual tunneling.

## Key findings

- The simplest tunneling approach does not describe tunneling but a WKB approximation.
- The temperature computed matches Hawking temperature but is not uniquely associated with Hawking radiation.
- Similar temperatures can occur in flat spacetime without curvature.

## Abstract

I consider the problem of reconciling "tunneling" approaches to black-hole radiation with the treatment by quantum field theory in curved space-time. It is not possible to do this completely, but using what appears to be the most direct and natural correspondence, the simplest case of such an approach does not describe a tunneling process but rather a WKB approximation to a two-point function. What it computes is a sort of rescaled Unruh temperature associated with world-lines tracing Killing trajectories near the horizon. This temperature is numerically equal to the Hawking temperature, but at this point no argument is known which identifies it with the Hawking effect; indeed, the same temperature can exist when no curvature is present.