Optical appearance of the Schwarzschild black hole in the string cloud context*

Abstract

The image of a black hole (BH) consists of direct and secondary images that depend on the observer position. We investigate the optical appearance of a Schwarzschild BH in the context of a string cloud to reveal how the BH's observable characteristics are influenced by the inclination angle, string cloud parameter, and impact parameter. Following Luminet's work [Astron. Astrophys. 75, 228 (1979)], we adopt a semi-analytic method to calculate the total bending angle of the light ray and derive the direct and secondary images of the Schwarzschild string cloud BH. Our results show that an increase in the inclination angle leads to a more pronounced separation of the images. We consider the gravitational redshift and present the redshift distribution of the direct image while illustrating the flux distribution. We observe that the direct image exhibits blueshift and redshift simultaneously, and the asymmetry of the flux distribution increases with the inclination angle. Finally, we obtain the Schwarzschild string cloud BH image via a numerical simulation, which provides an approximate illustration of the EHT resolution.

Photon orbits and phase transition for Letelier AdS black holes immersed in perfect fluid dark matter*

“…The criticality and thermal phase transition behavior was explored in the string cloud background in the presence of an additional field [38]. Another study was also devoted to the shadow analysis for the Letelier spacetime [39,40], whereas the others were studied in another contexts [41][42][43][44][45][46][47][48][49][50][51][52][53]. The Letelier spacetime in a spherically symmetric case is obtained with a gauge invariant model of an array of a cloud of strings coupled to gravity in the framework of Einstein's general relativity.…”