Shaving off soft hairs and the black hole image memory effect

TL;DR

This paper investigates how soft hair on Kerr black holes affects their images, revealing effects like rotation, dilation, and drifting that depend on angular directions and could serve as observational evidence.

Contribution

It introduces the concept of the image memory effect caused by soft hair, linking black hole physics with observable image changes and estimating its magnitude for spinning black holes.

Findings

Black hole images are rotated, dilated, and drifted due to soft hair effects.

The image memory effect magnitude scales with black hole mass and spin.

Detection of the effect is limited by current angular resolution capabilities.

Abstract

Soft hairs of black holes are the Noether charges associated with the generalized Bondi-Metzner-Sachs symmetries. In this work, the images of soft-haired Kerr black holes are studied. For an eternal black hole, the image is rotated, dilated, and drifting compared to that of the bald counterpart in the celestial plane. The rotation and the dilation are independent of time, while the drifting occurs at a constant speed and in a fixed direction. These effects all depend on angular directions. The soft hair of an astronomical black hole can change due to the emission of gravitational or electromagnetic waves from various physical processes occurring in the vicinity of the horizon. Then, the image roams in the observer's view, causing the image memory effect, the smoking gun for the existence of soft hair. The magnitude of the image memory effect of a huge, spinning black hole accompanied by a much smaller one is estimated. It turns out that this effect is proportional to the mass of the large black hole, increases with its spin, but decreases with the mass ratio. Due to the limited angular resolution of current and future detectors, this effect is hard to detect if the impact of cosmological expansion is ignored.