Shadow of a black hole surrounded by dark matter (1905.00064v3)

Abstract: We consider a simple spherical model consisting of a Schwarzschild black hole of mass $M$ and a dark matter of mass $\Delta M$ around it. The general formula for the radius of black-hole shadow has been derived in this case. It is shown that the change of the shadow is not negligible, once the effective radius of the dark matter halo is of order $\sim \sqrt{3 M \Delta M}$. For this to happen, for example, for the galactic black hole, the dark matter must be concentrated near the black hole. For small deviations from the Schwarzschild limit, the dominant contribution into the size of a shadow is due to the dark matter under the photon sphere, but at larger deviations, the matter outside the photon sphere cannot be ignored.

• The paper derives a general formula for the shadow radius in a Schwarzschild black hole surrounded by dark matter, showing significant effects when the halo’s effective radius is comparable to the scale sqrt(3MΔM).
• The analysis distinguishes three scenarios based on the photon sphere's position relative to the dark matter, clarifying when the shadow mimics a standard geometry or reflects the cumulative mass effects.
• The study highlights that while extended dark matter minimally alters the shadow, a concentrated dark matter halo near the black hole may produce detectable deviations for astrophysical observations.

Analysis of Black Hole Shadows in the Presence of Dark Matter

The paper, "Shadow of a black hole surrounded by dark matter," by R. A. Konoplya, presents an analytical exploration of the influence of a spherical distribution of dark matter on the shadow of a Schwarzschild black hole. The paper is built upon a conceptual model where a blithely spherical dark matter halo encircles a central black hole, facilitating the derivation of the general formula for the shadow's radius in such a configuration. Through a series of analytical and graphical solutions, the research offers insights into how the dark matter distribution impacts the perception of black hole shadows, a theoretical pursuit compelled by recent advancements and observations like those by the Event Horizon Telescope.

Key Findings

• The paper derives a general formula for the shadow radius when a Schwarzschild black hole is enveloped by dark matter with an effective mass, $\Delta M$. The results suggest that significant changes in the shadow's size are feasible only when the effective radius of the dark matter halo, $\Delta r_s$, is of the order $\sim \sqrt{3 M \Delta M}$.
• The author distinguishes three scenarios based on the location of dark matter relative to the black hole's photon sphere:
  1. When the photon sphere resides entirely within the interior of the dark matter, the shadow mimics that of a standard Schwarzschild geometry with negligible dark matter influence.
  2. When the photon sphere is outside the dark matter distribution, the shadow reflects the cumulative mass of the black hole and the dark matter.
  3. The non-trivial scenario is when the photon sphere exists within the dark matter halo, wherein it's suggested that the shadow's size indeed varies significantly due to the integration of the mass function within the dark matter region.

• The paper concludes that although dark matter in galactic halos cannot substantially alter the black hole shadow due to its vast distribution across extended radii, a concentrated mass of dark matter near the black hole may lead to observable deviations. Such deviations explicitly depend on the characteristics and spatial density of the dark matter distribution.

Theoretical Implications

This investigation contributes to the broader discourse on black hole physics, specifically in theoretical astrophysics and general relativity, by integrating the concept of dark matter's gravitational effects within standard black hole models. The research posits that dark matter's role is noteworthy primarily when its distribution is acutely dense at proximity to the black hole, prompting a reconsideration of shadow calculations in different theoretical gravitational frameworks.

Practical Implications

With emerging technologies like the Event Horizon Telescope providing increasingly precise measurements of black hole shadows, understanding potential alterations due to environmental factors, such as dark matter, is crucial. Such insights may aid in distinguishing between various configurations of dark matter around black holes in real-world observations, potentially informing the search for dark matter signatures across cosmic environments.

Future Directions

The research hints at avenues for expanding this model to encompass more complex distributions and interactions, such as non-spherical halos, rotating black holes, and various dark matter states. Future work may also explore numerical simulations that can corroborate these analytical findings under diverse astrophysical scenarios. Furthermore, the investigation into high-density dark matter is likely to continue, probing into how shadow observations might unveil unknown characteristics of both black holes and their enigmatic dark matter surroundings.

In essence, Konoplya's research underscores that while traditional interpretations of black hole shadows in the context of standard General Relativity remain largely undisturbed by neighboring dark matter, future observational and model advancements could potentially reveal broader intricacies in the spacetime tapestry surrounding black holes.