Towards rotating 2-2-holes

TL;DR

This paper explores the theoretical possibility of rotating 2-2-holes, horizonless objects in quadratic gravity, by developing approximate solutions to understand their properties and potential as black hole alternatives.

Contribution

It introduces a method to find approximate rotating solutions for 2-2-holes using an inverse size expansion parameter, advancing understanding of their structure.

Findings

Leading order solutions suggest possible interior structures of rotating 2-2-holes.

The approach provides a foundation for further detailed modeling of rotating horizonless objects.

Results support the viability of 2-2-holes as black hole mimickers in quadratic gravity.

Abstract

Static 2-2-hole solutions of quadratic gravity have been investigated to be a possible horizonless replacement for black holes as the endpoint of gravitational collapse. Realistically such objects will form with spin, but rotating 2-2-hole solutions are currently not known. We take some steps here to explore the existence and properties of such solutions. We employ an expansion of the field equations where the expansion parameter is inversely related to the size of the object. This expansion parameter appears explicitly in the trial metrics, and we are able to find solutions of the leading order field equations. These vacuum solutions are candidates to describe most of the interior of a rotating 2-2-hole.