Parameterizations of black-hole spacetimes beyond circularity

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.

agrees with version published in CQG

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Cited by in corpus (8)

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• Regularized Stable Kerr Black Hole: Cosmic Censorships, Shadow and Quasi-Normal Modes
• Universal signatures of singularity-resolving physics in photon rings of black holes and horizonless objects
• Instability of spherically-symmetric black holes in Quadratic Gravity
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• A novel test of gravity via black hole eikonal correspondence
• Testing black hole equatorial reflection symmetry using Sgr A* shadow images
• Identifying the Event Horizons of Parametrically Deformed Black-Hole Metrics