Non-singular rotating black hole with a time delay in the center

TL;DR

This paper explores constructing a rotating non-singular black hole with a central time delay, showing that direct modification of the metric is necessary to avoid curvature divergences, and analyzes various properties of such black holes.

Contribution

It demonstrates that introducing a time delay directly into the rotating non-singular black hole metric is essential to maintain finiteness, extending previous models by Bambi and Modesto.

Findings

Curvature divergences reappear when applying the Newman-Janis algorithm to a modified Hayward black hole.

Directly incorporating the time delay into the rotating metric preserves regularity.

The study details the deformation of the ergosphere and the impact of quantum gravity scale on extremal black holes.

Abstract

As proposed by Bambi and Modesto, rotating non-singular black holes can be constructed via the Newman-Janis algorithm. Here we show that if one starts with a modified Hayward black hole with a time delay in the centre, the algorithm succeeds in producing a rotating metric, but curvature divergences reappear. To preserve finiteness, the time delay must be introduced directly at the level of the non-singular rotating metric. This is possible thanks to the deformation of the inner stationarity limit surface caused by the regularisation, and in more than one way. We outline three different possibilities, distinguished by the angular velocity of the event horizon. Along the way, we provide additional results on the Bambi-Modesto rotating Hayward metric, such as the structure of the regularisation occurring at the centre, the behaviour of the quantum gravity scale alike an electric charge in decreasing the angular momentum of the extremal black hole configuration, or details on the deformation of the ergosphere.