# Late time approach to Hawking radiation: terms beyond leading order

## TL;DR

This paper investigates the late-time behavior of Hawking radiation beyond the leading order, revealing that higher order terms decay more slowly than expected and contain information about black hole formation.

## Contribution

It introduces a method to analyze higher order terms in Hawking radiation and demonstrates their slower decay, providing insights into black hole formation information.

## Key findings

- Higher order terms decay as a power law, not exponentially.
- Numerical verification in 2D and 4D black hole models.
- Higher order terms encode information about black hole formation.

## Abstract

Black hole evaporation is studied using wave packets for the modes. These allow for approximate frequency and time resolution. The leading order late time behavior gives the well known Hawking radiation that is independent of how the black hole formed. The focus here is on the higher order terms and the rate at which they damp at late times. Some of these terms carry information about how the black hole formed. A general argument is given which shows that the damping is significantly slower (power law) than what might be naively expected from a stationary phase approximation (exponential). This result is verified by numerical calculations in the cases of 2D and 4D black holes that form from the collapse of a null shell.