# Numerical computation of electromagnetically sourced nonlinear tails

## TL;DR

This paper numerically investigates nonlinear electromagnetic effects on black hole ringdown, revealing second-order gravitational tails that decay slower than linear ones, potentially impacting multi-messenger astrophysical observations.

## Contribution

It introduces a numerical method to compute second-order gravitational tails induced by electromagnetic sources in black hole environments, highlighting their decay rates and significance.

## Key findings

- Second-order tails decay as t^{-2l-2} at fixed position.
- Tails decay as u^{-l-3} at null infinity.
- Nonlinear tails decay slower than linear counterparts.

## Abstract

Amazingly, recent studies indicate that nonlinear effects are of great significance for modelling black hole ringdown. Transient electromagnetic events in the astrophysical environment are typically high energetic, potentially responsible for some nonlinearities in ringdown. Motivated by the desire to understand these nonlinearities, we solve the inhomogeneous Bardeen-Press-Teukolsky equation numerically, and find second-order gravitational tails induced by an electromagnetic source. Our results suggest that the second-order tails of curvature perturbations with multipole numbers $l\geq4$ decay as $t^{-2l-2}$ at fixed spatial position and $u^{-l-3}$ in retarded-time $u$ at null infinity, slower than their linear counterparts, which can play a role in multi-messenger observations.