[Paper Review] Black hole surrounded by the pseudo-isothermal dark matter halo

Yi Yang, Dong Liu+3 more|arXiv (Cornell University)|Aug 10, 2023

Galaxies: Formation, Evolution, Phenomena126 references4 citations

TL;DR

This paper derives a rotating black hole solution surrounded by a pseudo-isothermal dark matter halo using the Newman-Janis method, analyzing its event horizon, null and time-like orbits, and shadow. Key results show that increasing spin distorts the black hole shadow significantly, while dark matter density has minimal impact on the shadow or event horizon, suggesting Kerr-like observational signatures despite dark matter presence.

ABSTRACT

The abundance of dark matter in the actual universe motivates us to construct the black hole spacetime enveloped by dark matter. In this paper, we derive a new spherically symmetric black hole surrounded by the pseudo-isothermal dark matter halo, and then explore the effects of the pseudo-isothermal halo profile on a rotating black hole at the M87 galactic center, aiming to achieve a black hole solution that aligns with those found in the real universe. Using the Newman-Janis method, we derive a rotating black hole solution encompassed by the pseudo-isothermal halo, which is consistent with observations of actual black holes that are believed to possess spin. Our investigation focuses on the impact of the pseudo-isothermal halo on the black hole event horizon, time-like and null orbits, as well as the black hole shadow. We find that as the spin parameter $a$ increases, the interval between the inner event horizon and the outer event horizon of the rotating black hole surrounded by the pseudo-isothermal halo in M87 diminishes. This leads to the formation of an extreme black hole. The presence of dark matter, however, has minimal effect on the event horizon. Moreover, in the M87 as the spin parameter $a$ increases, the black hole shadow deviates increasingly from a standard circle, with larger spin parameters causing more pronounced distortion relative to the standard circle. Surprisingly, we observe that the dark matter density has very little influence on the shadow of the black hole surrounded by the pseudo-isothermal halo in the M87. This study contributes to a deeper understanding of black hole structures and the role of dark matter in the universe.

Motivation & Objective

• To model a spherically symmetric black hole surrounded by a pseudo-isothermal dark matter halo using general relativity.
• To extend the Schwarzschild solution to a rotating black hole with a dark matter halo via the Newman-Janis method.
• To investigate the effects of the pseudo-isothermal halo on the event horizon, geodesics, and black hole shadow in the M87 galaxy context.
• To assess whether dark matter density significantly alters observable features like the black hole shadow.
• To explore the implications for distinguishing such black holes from Kerr black holes via shadow and gravitational wave observations.

Proposed method

• Adopt the pseudo-isothermal dark matter halo profile with parameters $\rho_0 = 6.9 \times 10^6 M_\odot/\text{kpc}^3$ and $r_0 = 91.2\,\text{kpc}$ to model the dark matter distribution.
• Use the Newman-Janis algorithm to generate a rotating black hole solution from the spherically symmetric metric, incorporating the halo profile.
• Compute the event horizon structure and analyze the separation between inner and outer horizons as a function of spin parameter $a$.
• Simulate null and time-like geodesics to study orbital dynamics near the black hole in the halo environment.
• Calculate the black hole shadow using the formalism of Xu et al., comparing with standard Schwarzschild and Kerr cases.
• Vary spin parameter $a$ and dark matter density $\rho_0$ to assess their influence on shadow shape and size.

Experimental results

Research questions

• RQ1 How does the presence of a pseudo-isothermal dark matter halo affect the event horizon structure of a rotating black hole in M87?
• RQ2 To what extent does the spin parameter $a$ distort the black hole shadow compared to the standard circular shadow of a Schwarzschild black hole?
• RQ3 Does the dark matter density $\rho_0$ significantly alter the shape or size of the black hole shadow?
• RQ4 How similar are the shadow characteristics of the halo-embedded rotating black hole to those of the standard Kerr black hole?
• RQ5 Can gravitational wave signals from such a black hole be distinguished from those of a Kerr black hole based on quasinormal modes?

Key findings

• As the spin parameter $a$ increases, the interval between the inner and outer event horizons of the rotating black hole in the pseudo-isothermal halo decreases, leading to the formation of an extreme black hole.
• The presence of dark matter has minimal effect on the location or structure of the event horizon, indicating that halo density does not significantly alter horizon properties.
• The black hole shadow deviates increasingly from a standard circle as $a$ increases, with larger spin values causing more pronounced distortion, especially on the left side of the shadow.
• Despite varying dark matter density $\rho_0$, the shadow remains nearly indistinguishable from that of a Kerr black hole, indicating very little influence of halo density on the shadow.
• The shadow of the rotating black hole with a pseudo-isothermal halo closely resembles the Kerr black hole shadow, suggesting observational degeneracy in shadow-based detection.
• The results imply that distinguishing such a halo-embedded black hole from a Kerr black hole via shadow imaging alone may be challenging, warranting further study of quasinormal modes in gravitational waves.