Distorted Local Shadows

TL;DR

This paper defines a local shadow for black holes, analyzes its shape for distorted Schwarzschild black holes, and finds that shadow deformations are more pronounced than horizon deformations, with unexpected inverse relationships.

Contribution

It introduces the concept of a local shadow for black holes and explores how distortions affect the shadow's shape, revealing new inverse deformation relationships.

Findings

Shadow deformations are larger than horizon deformations

Prolate horizon distortions lead to oblate shadow distortions

The horizon appears more rigid than the shadow

Abstract

We introduce the notion of a local shadow for a black hole and determine its shape for the particular case of a distorted Schwarzschild black hole. Considering the lowest-order even and odd multiple moments, we compute the relation between the deformations of the shadow of a Schwarzschild black hole and the distortion multiple moments. For the range of values of multiple moments that we consider, the horizon is deformed much less than its corresponding shadow, suggesting the horizon is more `rigid'. Quite unexpectedly we find that a prolate distortion of the horizon gives rise to an oblate distortion of the shadow, and vice-versa.