# Scalar Fields in Black Hole Spacetimes

## TL;DR

This paper numerically investigates the late-time behavior of scalar fields in black hole spacetimes, revealing power-law tails outside and oscillatory, potentially unstable behavior inside, especially in extremal Kerr black holes.

## Contribution

It provides new insights into the interior dynamics of scalar fields in black holes, including the first detailed numerical analysis of oscillations and instabilities inside the horizon.

## Key findings

- Power-law tails observed outside the black hole.
- Oscillatory behavior inside the horizon linked to multipole index.
- Indications of horizon instability in extremal Kerr black holes.

## Abstract

The time-evolution of matter fields in black hole exterior spacetimes is a well-studied subject, spanning several decades of research. However, the behavior of fields in the black hole interior spacetime, has only relatively recently begun receiving some attention from the research community. In this paper, we numerically study the late-time evolution of scalar fields in both Schwarzschild and Kerr spacetimes, including the black hole interior. We recover the expected late-time power-law "tails" on the exterior (null infinity, time-like infinity and the horizon). In the interior region, we find an interesting oscillatory behavior that is characterized by the multipole index $\ell$ of the scalar field. In addition, we also study the extremal Kerr case and find strong indications of an instability developing at the horizon.