Shadows and amplitude luminosity of an embedded rotating black hole

TL;DR

This work develops a covariant, model-independent framework based on Nash's embedding theorem to study a rotating black hole embedded in a five-dimensional bulk via the Gürses–Gürsey metric. By treating extrinsic curvature as a dynamical degree of freedom, the authors derive a Kerr-like solution with a tidal-charge–like parameter $\alpha_0$ that arises from extrinsic geometry, affecting horizon structure, ISCO behavior, and the effective energy–momentum content. They implement Hamilton–Jacobi geodesic analysis to obtain geodesic integrals, compute horizon conditions, and perform ray-traced shadow and visibility simulations for M87$^*$ using the AART code, finding Kerr-consistent results in the appropriate limit but with potential deviations detectable by future high-resolution VLBI. Cosmological matching ties $\alpha_0$ to large-scale perturbations, and the associated Komar mass and EMT analyses reveal a repulsive sector from embedding that violates the SEC, suggesting novel regularization and phenomenological implications. Overall, the embedded Kerr-like geometry preserves core Kerr features while offering testable higher-dimensional imprints in horizon, shadow, and interference patterns.

Abstract

We investigate a rotating black hole embedded in a five-dimensional flat bulk by extending the Kerr metric through the Gurses-Gursey line element. Employing Boyer-Lindquist coordinates, we reinterpret the black hole as a charged-like object in five dimensions and analyze its horizon structure and shadow morphology. Our results reveal that the shadow is shaped by an axially symmetric gravitational field modulated by an extrinsic curvature term arising from the higher-dimensional embedding. Simulations demonstrate that the visibility amplitude and shadow profile of the Gurses-Gursey black hole align with Event Horizon Telescope observations of M87 in the Kerr limit, while also allowing measurable deviations that could be probed by future high-resolution experiments.

Figures (3)

• Figure 1: Effective potential for different values of $L$ and $E$ for massive particles $\mu=1.0$ for each spin $a$. The ISCO are also represented for each spin $a$, accordingly.
• Figure 2: Image pixels $(\alpha, \beta)$ produced for different values of spin parameters (the top, middle and bottom row indicate a$=[0,0.3,0.94]$, respectively) and inclination angles $i = 17^\circ, 45^\circ, 85^\circ$.
• Figure 3: Schematic showing visibility amplitude as a function of baseline length for two different azimuthal angles, $\varphi = 0^\circ$ and $\varphi = 90^\circ$ at different inclinations, ($i = 17^\circ, 45^\circ, 85^\circ$). From top to bottom rows, we have the spin parameters $a=0,0.3,0.94$, respectively