# A Vector Field Method for Radiating Black Hole Spacetimes

## TL;DR

This paper introduces a vector field technique for analyzing radiating black hole spacetimes, providing sharp decay estimates for scalar fields in these complex gravitational backgrounds.

## Contribution

It develops a new commuting vector field method applicable to a broad class of radiating spacetimes, including perturbations of Minkowski space, enhancing analysis of scalar fields.

## Key findings

- Sharp peeling estimates for linear scalar fields
- Extension to nonlinear (null form) scalar fields
- Applicable to long-range perturbations of Minkowski space

## Abstract

We develop a commuting vector field method for a general class of radiating spacetimes. The metrics considered are certain long range perturbations of Minkowski space including those constructed from global stability problems in general relativity. Our method provides sharp peeling estimates for solutions to both linear and nonlinear (null form) scalar fields.