Parameterizations of black-hole spacetimes beyond circularity

TL;DR

This paper develops a comprehensive parameterization framework for axisymmetric, stationary black-hole spacetimes that includes non-circular geometries, enhancing modeling of deviations from Kerr black holes and their observational signatures.

Contribution

It introduces a new parameterization that encompasses non-circular spacetimes, including those in horizon-penetrating coordinates, and compares it to existing models with additional symmetry assumptions.

Findings

Existing parameterizations are special cases of the new framework.

Horizon-penetrating coordinates are better suited for non-circular deviations.

Certain non-circular deviations cannot be regularized, supporting regular black hole models.

Abstract

We discuss parameterizations of black-hole spacetimes in and beyond General Relativity in view of their symmetry constraints: within the class of axisymmetric, stationary spacetimes, we propose a parameterization that includes non-circular spacetimes, both in Boyer-Lindquist as well as in horizon-penetrating coordinates. We show how existing parameterizations, which make additional symmetry assumptions (first, circularity; second, a hidden constant of motion), are included in the new parameterization. Further, we explain why horizon-penetrating coordinates may be more suitable to parameterize non-circular deviations from the Kerr geometry. Our investigation is motivated by our result that the regular, spinning black-hole spacetimes proposed in [1,2] are non-circular. This particular deviation from circularity can result in cusps, a dent and an asymmetry in the photon rings surrounding the black-hole shadow. Finally, we explore a new class of non-circular deviations from Kerr black holes, which promote the spin parameter to a function, and find indications that regularity cannot be achieved in this setting. This result strengthens the case for regular black holes based on a promotion of the mass parameter to a function.