Strong Gravitational Lensing Effects of the Rotating Short-Haired Black Hole and Constraints from EHT Observations

TL;DR

This paper investigates the strong gravitational lensing effects of rotating short-haired black holes, constrains their parameters using EHT observations, and highlights significant differences from Kerr black holes in observable phenomena.

Contribution

It systematically analyzes lensing effects in rotating short-haired black holes and constrains their hair parameter using observational data, offering new insights into alternative black hole models.

Findings

Event horizon and photon-orbit radii decrease with hair parameter Q_m.

Lensing coefficients vary with spin parameter a, affecting image properties.

Time delay deviations can reach dozens of hours, aiding model differentiation.

Abstract

For the short hairs that have a significant impact only near the event horizon, studying their strong gravitational lensing effects is of great significance for revealing the properties of these hairs. In this study, we systematically investigated the strong gravitational lensing effects in the rotating short-haired black hole and constrained its hair parameter $Q_m$. Specifically, \(Q_m\) causes the event horizon radius, photon - orbit radius, and impact parameter to be lower than those of the Kerr black hole. Regarding the lensing coefficients \(\bar{a}\) and \(\bar{b}\), as the spin parameter \(a\) increases, \(\bar{a}\) shows an increasing trend, while \(\bar{b}\) shows a decreasing trend. In the observational simulations of M87* and Sgr A*, the angular position and angular separation of the relativistic image increase with the increase of \(a\), while the magnification of the image shows an opposite trend. The existence of \(Q_m\) only intensifies these trends, while parameter $k$ suppresses such tendencies. More importantly, the rotating short-haired black hole exhibits a significant difference in time delay compared to other black hole models. Especially in the simulation of M87*, the time delay deviation between the rotating short-haired black hole and the Kerr black hole, as well as the Kerr-Newman black hole, can reach dozens of hours. Through a comparative analysis with the observational data from the EHT, we effectively constrain the parameter space of the rotating short-haired black hole. The results indicate that this model has potential application prospects in explaining cosmic black hole phenomena and provides a possible theoretical basis for differentiating between different black hole models.