Trumpet Slices in Kerr Spacetimes

TL;DR

This paper introduces a new family of analytical coordinate systems for Kerr black holes, enabling the first analytical stationary trumpet slices for rotating and charged black holes with a cosmological constant.

Contribution

It presents a novel coordinate system and a formalism to analytically describe stationary trumpet slices in Kerr spacetimes, including charged and cosmological constant cases.

Findings

First analytical stationary trumpet slices for rotating black holes.

Explicit metric functions for the new trumpet slices.

Analysis of the trumpet surface geometry.

Abstract

We introduce a new time-independent family of analytical coordinate systems for the Kerr spacetime representing rotating black holes. We also propose a (2+1)+1 formalism for the characterization of trumpet geometries. Applying this formalism to our new family of coordinate systems we identify, for the first time, analytical and stationary trumpet slices for general rotating black holes, even for charged black holes in the presence of a cosmological constant. We present results for metric functions in this slicing and analyze the geometry of the rotating trumpet surface.