Imaging the destruction of a rotating regular black hole

TL;DR

The paper investigates how rotating regular black holes, specifically the Ghosh RBH, and their superspinar counterparts would appear when surrounded by a thin accretion disk, and how the horizon-destruction transition via a collapsing null shell affects observed images. It employs a Hamiltonian-based ray-tracing framework in stationary and dynamical spacetimes, a GLM emissivity profile with an ISCO-based inner boundary, and analyzes redshift effects and photon-ring structures. Key findings show that the Ghosh RBH images closely resemble Kerr images with k-driven ISCO and photon-ring shifts, while superspinars reveal inner secondary images that depend on spin and inclination; during destruction, the image transition proceeds gradually with a characteristic timescale Δt/M ≈ 60, though a sudden light burst may accompany horizon dissolution. The results offer observational signatures and caveats for testing rotating regular black holes and horizon-physics scenarios with current or future very-long-baseline interferometry, highlighting the relevance of transition timescales for very massive supermassive black holes and the importance of radiative-transfer realism in modeling superspinars.

Abstract

A regular black hole, unconstrained by the weak cosmic censorship conjecture, can exceed its critical spin limit and transition into a superspinar. In this paper, we investigate the observational appearance of a rotating regular black hole, specifically the Ghosh black hole and its superspinar counterpart, when surrounded by a thin accretion disk. The resulting images reveal distinct features: the black hole closely resembles its Kerr counterpart with slight deviations, while the superspinar configuration exhibits an inner photon ring structure. Furthermore, we investigate the image transition of the Ghosh black hole that has recently been destroyed by a collapsing null shell carrying a specific angular momentum. The results indicate that, apart from a possible sudden burst of light, the inner photon ring undergoes gradual transitions over time, with the transition times depending on the additional angular momentum gained by the black hole. Our findings also suggest that the transition timescale becomes significant for supermassive black holes, with masses at least less than about twice that of M87*.

Figures (22)

• Figure 1: The critical spin value $a_c/M$ (red line) and its corresponding extremal horizon radius $r_H^e/M$ (blue line) as functions of $k/M$. The grey shaded area depicts the BH configuration where the spacetime contains horizon(s), while the region outside (with $a>0$) corresponds to the superspinar configuration.
• Figure 2: A sketch of the Penrose diagram for extremal (left) and non-extremal (right) BH destruction with a collapsing null shell (red dashed lines). Region I represents the spacetime exterior to the BH, while Region II is the region between the outer horizon $r_H^+$ and the inner horizon $r_H^-$. In the extremal BH, $r_H^-$ and $r_H^+$ coincide at $r_H^e$, and thus Region II does not exist. Region III corresponds to the BH interior, and Region IV denotes the superspinar spacetime.
• Figure 3: The absolute value of the Kretschmann scalar in logarithmic scale for $\delta/M = 5 \times 10^{-3}$, $k/M=0.01$, and $a_0=a_c$, with $\sigma_s = 10^{-4}$ (left column) and $\sigma_s = 10^{-3}$ (right column), shown as a function of $r$ and $u$ near $u_c$.
• Figure 4: The quantity $T_{uu}/(-g_{uu})$ at $\theta = \pi/3$ for $\delta/M = 5 \times 10^{-3}$, $k/M = 0.01$, and $a_0 = a_c$, with $\sigma_s = 10^{-4}$ (left column) and $\sigma_s = 10^{-3}$ (right column), plotted as a function of $r$ and $u$ near $u_c$. The black dashed region indicates where the WEC is violated, while the green dashed region marks the ergoregion where $-g_{uu} \leq 0$.
• Figure 5: A 2D schematic of the pinhole ray-tracing procedure. Light rays (yellow curves) are traced backward from the observer, located at a distance $r_0$ from the BH, and directed toward the BH. The accretion disk (orange thick line) lies in the equatorial plane ($\theta=\pi/2$) and follows a retrograde orbit relative to the spin of the BH.