A new way to see inside black holes

TL;DR

This paper computes and visualizes all independent curvature invariants of rotating, charged black holes, providing a coordinate-invariant depiction that reveals a more complex and beautiful internal structure than traditional coordinate-based illustrations.

Contribution

It is the first to calculate and plot all independent curvature invariants of rotating, charged black holes, offering a new, coordinate-invariant perspective on their internal structure.

Findings

Curvature invariants reveal complex internal landscape

Coordinate-invariant depiction differs from traditional views

Enhanced understanding of black hole geometry

Abstract

Black holes are real astrophysical objects, but their interiors are hidden and can only be "observed" through mathematics. The structure of rotating black holes is typically illustrated with the help of special coordinates. But any such coordinate choice necessarily results in a distorted view, just as the choice of projection distorts a map of the Earth. The truest way to depict the properties of a black hole is through quantities that are coordinate-invariant. We compute and plot all the independent curvature invariants of rotating, charged black holes for the first time, revealing a landscape that is much more beautiful and complex than usually thought.