[Paper Review] Optical properties of a nonlinear magnetic charged rotating black hole surrounded by quintessence with a cosmological constant

Chen Yuan, He-Xu Zhang+2 more|arXiv (Cornell University)|Sep 6, 2020

Black Holes and Theoretical Physics27 references9 citations

TL;DR

This paper investigates the optical properties of a nonlinear magnetic charged rotating black hole embedded in a quintessence field with a non-zero cosmological constant, using numerical solutions to analyze horizons, photon regions, and shadow shapes. Key findings show that increasing rotation (a) and magnetic charge (Q) distort and elongate the shadow, while quintessence and cosmological constant reduce its size, offering observational signatures for dark energy and modified gravity in strong-field regimes.

ABSTRACT

In this paper,we discuss optical properties of the nonlinear magnetic charged black hole surrounded by quintessence with a non-zero cosmological constant $Λ$. Setting the state parameter $ω=-3/2$ , we studied the horizon, the photon region and the shadow of this black hole. It turned out that for a fixed quintessential parameter $γ$, in a certain range, with the increase of the rotation parameter $a$ and magnetic charge $Q$, the inner horizon radius increases while the outer horizon radius decreases. And the cosmological horizon $r_Λ$ decrease when $γ$ or $Λ$ incease and increase slightly with increasing $a$ and $Q$. The shapes of photon region were then studied and depicted through graphical illustrations. Finally, we discussed the effects of the quintessential parameter $γ$ and the cosmological constant $Λ$ on the shadow cast by this balck hole with a fixed observer position.

Motivation & Objective

• To analyze the optical properties of a nonlinear magnetic charged rotating black hole in the presence of quintessence and a cosmological constant.
• To investigate how the quintessence parameter γ and cosmological constant Λ affect the black hole's horizons, photon region, and shadow morphology.
• To provide theoretical predictions for shadow shapes that could be tested by future observations, such as those from the Event Horizon Telescope.

Proposed method

• Derivation of the metric for a nonlinear magnetic charged rotating black hole surrounded by quintessence with a cosmological constant, using a modified Einstein-Maxwell action with a specific equation of state for quintessence (ω = -3/2).
• Numerical solution of horizon equations to determine the behavior of inner, outer, and cosmological horizons (r₊, r₋, rΛ) as functions of rotation (a), magnetic charge (Q), γ, and Λ.
• Computation of the photon region via spherical lightlike geodesics, using the constants of motion R and Θ derived from the Hamilton-Jacobi equation.
• Application of stereographic projection to map the shadow boundary onto a celestial plane using coordinates x and y derived from Υ and Φ.
• Use of fixed observer position at r₀ = 50, θ₀ = π/2 to ensure consistent shadow visualization across parameter variations.
• Graphical analysis of shadow shapes under varying a, Q, γ, and Λ, with emphasis on distortion and size changes.

Experimental results

Research questions

• RQ1 How does the presence of quintessence and a cosmological constant affect the structure of the black hole horizons in a nonlinear magnetic charged rotating black hole?
• RQ2 How do the rotation parameter a and magnetic charge Q influence the shape and size of the photon region and shadow?
• RQ3 What is the impact of the quintessence parameter γ and cosmological constant Λ on the shadow's size and deformation?
• RQ4 Can the shadow of such a black hole serve as a probe for dark energy and modified gravity in strong-field gravity?
• RQ5 How do the horizons evolve as a and Q increase, and what are the conditions for extremality or horizon disappearance?

Key findings

• For fixed γ, increasing rotation parameter a causes the inner horizon radius to increase and the outer horizon radius to decrease, while the cosmological horizon rΛ increases slightly.
• For fixed a, increasing magnetic charge Q causes the inner and outer horizons to approach and eventually disappear when Q > Q_E, indicating a critical extremal limit.
• The cosmological horizon rΛ significantly decreases with increasing γ or Λ, while showing only a slight increase with higher a or Q.
• The shadow becomes more elongated and distorted with increasing a, while increasing Q reduces the shadow size and induces additional distortion.
• The intensity of the quintessence field (γ) and the cosmological constant Λ both reduce the shadow size, with γ having a more pronounced effect on shadow diminution.
• Photon region shapes vary significantly with γ, exhibiting two distinct categories of behavior, and the shadow boundary is determined by light rays asymptotically approaching spherical lightlike geodesics at r_p.