Black holes immersed in dark matter: energy condition and sound speed

TL;DR

This paper investigates how dark matter around black holes affects energy conditions and sound speeds, revealing violations of physical constraints and proposing a cutoff to ensure realistic models.

Contribution

It introduces a detailed analysis of energy conditions and sound speeds in black hole environments with dark matter, highlighting violations and proposing a subluminal cutoff.

Findings

Violations of energy conditions near black holes with dark matter

Superluminal sound speeds occur in certain configurations

Introducing a cutoff restores physical plausibility

Abstract

In this work, we study the impact of the environment around a black hole in detail. We introduce non-vanishing radial pressure in a manner analogous to compact stars. We examine both isotropic and anisotropic fluid configurations with and without radial pressure respectively. Our focus extends beyond just dark matter density to the vital role of the energy condition and sound speed in the spacetime of a black hole immersed in matter. In cases of anisotropic pressure with vanishing radial pressure, all profiles violate the dominant energy condition near the BH, and the tangential sound speed exceeds light speed for all dark matter profiles. In our second approach, without assuming vanishing radial pressure, we observe similar violations and superluminal sound speeds. To rectify this, we introduce a hard cutoff for the sound speed, ensuring it remains subluminal. As a consequence, the energy condition is also satisfied. However, this results in increased density and pressure near the BH. This raises questions about the sound speed and its impact on the density structure, as well as questions about the validity of the model itself. With the matter distribution, we also compute the metric for different configurations. It reveals sensitivity to the profile structure. The metric components point towards the horizon structure.