A Multipole-Based Framework for Kerr Black Hole Mimickers: From General Construction to a Specific Case of Study

TL;DR

This paper introduces a systematic framework for designing energy-momentum tensors that produce gravitational fields mimicking Kerr black holes, using linearized gravity and anisotropic rotating fluids, with detailed phenomenological analysis.

Contribution

It develops a new method to construct energy-momentum tensors with specific multipolar structures, enabling the modeling of black hole mimickers within linearized gravity.

Findings

Successfully reproduces Kerr multipolar structure with anisotropic fluid

Satisfies energy and causality conditions at linearized order

Provides insights into source and metric phenomenology compared to black holes

Abstract

We present a novel systematic framework for engineering energy-momentum tensors in linearized gravity that generate gravitational fields with a prescribed multipolar structure, aimed at modeling black hole mimickers. As a concrete example, we analyze an anisotropic rotating fluid with a Gaussian-like energy-density profile which, at linearized order, satisfies all energy and causality conditions while generating a gravitational field that exactly reproduces the multipolar structure of a Kerr black hole. We then investigate the phenomenology of both the source and the induced metric, comparing our findings with the corresponding black hole limit.