Second Order Scalar Invariants of the Riemann Tensor: Applications to Black Hole Spacetimes

TL;DR

This paper analyzes second order scalar invariants of the Riemann tensor, such as Kretschmann, Chern-Pontryagin, and Euler invariants, in black hole spacetimes, using Newman-Penrose formalism and gravitoelectromagnetism, with Kerr-Newman as an example.

Contribution

It introduces a novel analysis of these invariants in black hole spacetimes and establishes an analogy with electromagnetic invariants to identify regions of gravitoelectric or gravitomagnetic dominance.

Findings

Identification of regions with gravitoelectric or gravitomagnetic dominance.

Application of invariants to Kerr-Newman geometry.

Use of Newman-Penrose formalism and gravitoelectromagnetism.

Abstract

We discuss the Kretschmann, Chern-Pontryagin and Euler invariants among the second order scalar invariants of the Riemann tensor in any spacetime in the Newman-Penrose formalism and in the framework of gravitoelectromagnetism, using the Kerr-Newman geometry as an example. An analogy with electromagnetic invariants leads to the definition of regions of gravitoelectric or gravitomagnetic dominance.