Hernquist distribution of matter as a source of black-hole geometry

TL;DR

This paper investigates whether common galactic halo profiles, including Hernquist, can produce regular black-hole geometries under specific pressure conditions, finding that most do not, and instead support singular solutions.

Contribution

It demonstrates that the Hernquist and similar profiles do not produce regular black-hole solutions under the $P_{r} = - ho$ condition, highlighting limitations of this approach.

Findings

Hernquist profile does not yield regular black-hole geometries under the given condition.

Most common halo profiles support black-hole solutions with central singularities.

Regular geometries are not achievable for Hernquist and similar profiles with the imposed pressure condition.

Abstract

It was recently demonstrated that imposing the condition $P_{r} = -\rho$ on the radial pressure of a galactic halo can lead to regular black-hole solutions for certain density profiles, such as the Dehnen and Einasto models. In the present work, we show that some of the most commonly used halo profiles, including the Hernquist model, do not yield regular geometries under the same condition, but instead support black-hole solutions that retain a central singularity