Null fluid gravitational fields on Kerr manifolds and optical lifts of Sasaki structures

TL;DR

This paper provides an explicit parameterization of null fluid gravitational fields on Kerr manifolds, introduces a new solution-generating method for Einstein equations with null fluids, and resolves a conjecture on optical lifts of Sasaki structures.

Contribution

It offers a novel explicit parameterization of null fluid solutions on Kerr manifolds and solves a conjecture on optical lifts of Sasaki structures.

Findings

Constructed a large family of explicit Einstein metrics including Kerr black holes.

Developed a new method for solutions with null fluid energy-momentum tensor.

Proved a conjecture on the existence of smooth optical lifts for Sasaki CR structures.

Abstract

Building on the characterisation in [C. D. Hill, J. Lewandowski and P. Nurowski, Indiana Univ. Math. J. 57 (2008), 3131--3176] of 4-dimensional Lorentzian metrics adapted to an optical structure and satisfying the null fluid Einstein equations, we give an explicit parameterisation of this class under the assumption that the optical structure is of Kerr type. As immediate consequences, we obtain: (1) a new method for constructing solutions to the Einstein equations with a null fluid energy momentum tensor, yielding a large family of explicit metrics that naturally includes the classical Kerr black hole metrics and all Ricci flat examples described in [M. Ganji, C. Giannotti, G. Schmalz and A. Spiro, Ann. Physics 75 (2025), Paper No. 169908, 28]; (2) a solution to a conjecture in Hill, Lewandowski and Nurowski's paper on the local existence of smooth optical lifts in the case of Sasaki CR structures.