On the near horizon rotating black hole geometries with NUT charges

TL;DR

This paper constructs Ricci-flat metrics with NUT charges in four and five dimensions using conformal invariants, providing new near horizon geometries for extremal black holes with NUT parameters.

Contribution

It introduces a novel method to generate near horizon black hole geometries with NUT charges via conformal invariants, extending the understanding of extremal black hole structures.

Findings

Derived the d=4 near horizon Kerr-NUT black hole metric.

Constructed a five-parameter Ricci-flat metric in d=5.

Identified a specific metric candidate for the d=5 near horizon Myers-Perry black hole with NUT charge.

Abstract

The near horizon geometries are usually constructed by implementing a specific limit to a given extreme black hole configuration. Their salient feature is that the isometry group includes the conformal subgroup SO(2,1). In this work, we turn the logic around and use the conformal invariants for constructing Ricci-flat metrics in d=4 and d=5 where the vacuum Einstein equations reduce to a coupled set of ordinary differential equations. In four dimensions the analysis can be carried out in full generality and the resulting metric describes the d=4 near horizon Kerr-NUT black hole. In five dimensions we choose a specific ansatz whose structure is similar to the d=5 near horizon Myers-Perry black hole. A Ricci-flat metric involving five arbitrary parameters is constructed. A particular member of this family, which is characterized by three parameters, seems to be a natural candidate to describe the d=5 near horizon Myers-Perry black hole with a NUT charge.