[Paper Review] Shadow casted by a twisted and rotating black hole

Songbai Chen, Jiliang Jing|arXiv (Cornell University)|Oct 4, 2016

Astrophysical Phenomena and Observations3 citations

TL;DR

This paper investigates the shadow cast by a twisted rotating black hole—a vacuum solution in 4D Einstein gravity with a rotation parameter but no total angular momentum. Despite the rotation parameter, the shadow remains a round disk independent of observer inclination, and both the photon sphere radius and shadow size monotonically increase with rotation, resembling a static black hole rather than a Kerr-like one.

ABSTRACT

Zhang have obtained recently a twisted rotating black hole metric, which is a vacuum solution in four-dimensional Einstein gravity. This black hole solution has a rotation parameter, but without the total angular moment. Here, we have investigated the shadow casted by a twisted rotating black hole. Our results show that the shape of the shadow of the twisted rotating black hole is a standard round disk and does not depend on the inclination angle of the observer. It means that although the twisted rotating black hole has a rotation parameter, its shadow possesses the same behaviors as the common static black hole rather than the usual Kerr-like black holes. Moreover, we find that the marginally circular orbit radius of photon is independent of the direction of photon around the black hole. The value of the marginally circular orbit radius of photon and the size of shadow increase monotonously with the rotation parameter.

Motivation & Objective

• To analyze the shadow morphology of a twisted rotating black hole, a novel vacuum solution in 4D Einstein gravity.
• To investigate how the rotation parameter influences the shadow shape and size despite the absence of total angular momentum.
• To determine whether the shadow exhibits behaviors typical of Kerr-like black holes or resembles static black holes.
• To examine the properties of the marginally stable photon orbit and its dependence on direction and rotation.

Proposed method

• The study employs the twisted rotating black hole metric recently derived by Zhang, which satisfies the vacuum Einstein equations in four dimensions.
• The shadow is calculated using the null geodesic equations to trace photon trajectories near the black hole.
• The observer's inclination angle is varied to assess its effect on the shadow's apparent shape and size.
• The radius of the marginally stable circular photon orbit is computed using the effective potential method in the equatorial plane.
• The shadow boundary is determined by the critical impact parameters corresponding to photons escaping to infinity or plunging into the horizon.
• Numerical simulations are used to visualize the shadow and analyze its dependence on the rotation parameter and observer orientation.

Experimental results

Research questions

• RQ1 How does the shadow of a twisted rotating black hole differ from that of a standard Kerr black hole?
• RQ2 Does the shadow shape remain circular and independent of the observer's inclination angle despite the presence of a rotation parameter?
• RQ3 How does the radius of the marginally stable photon orbit vary with the rotation parameter and photon direction?
• RQ4 To what extent does the shadow size scale with the rotation parameter in the absence of total angular momentum?
• RQ5 Is the shadow behavior more similar to that of a static black hole or a rotating Kerr black hole?

Key findings

• The shadow of the twisted rotating black hole is a perfect circle, regardless of the observer's inclination angle.
• The shadow size increases monotonically with the rotation parameter, indicating a direct scaling relationship.
• The radius of the marginally stable circular photon orbit is independent of the photon's azimuthal direction around the black hole.
• The photon sphere radius grows with increasing rotation parameter, consistent with the increasing shadow size.
• Despite having a rotation parameter, the shadow's behavior closely resembles that of a static black hole rather than a Kerr-like rotating black hole.
• The absence of total angular momentum does not alter the circular symmetry of the shadow or the isotropy of the photon orbit radius.