# Kerr principal null directions from Bel--Robinson and Kummer surfaces

## TL;DR

This paper explores the geometric properties of Kerr spacetime, identifying principal null directions via Bel--Robinson and Kummer tensors, and discusses potential observational implications of constant curvature surfaces beyond the horizon.

## Contribution

It introduces a novel method to determine Kerr principal null directions using Bel--Robinson and Kummer tensors, extending understanding of spacetime invariants.

## Key findings

- Principal null directions can be derived from Bel--Robinson and Kummer tensors.
- Constant curvature surfaces extend beyond the Kerr horizon.
- Potential observational significance of these surfaces in non-minimally coupled matter fields.

## Abstract

In the Kerr geometry, we calculate various surfaces of constant curvature invariants. These extend well beyond the Kerr horizon, and we argue that they might be of observational significance in connection with non-minimally coupled matter fields. Moreover, we demonstrate that the principal null directions of the Kerr geometry can be obtained by projections involving either the Bel--Robinson or the Kummer tensor. We conjecture that this is also possible in more general settings.