The correspondence between shadow and test field in a four-dimensional charged Einstein–Gauss–Bonnet black hole

Abstract

In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a four-dimensional charged Einstein–Gauss–Bonnet black hole. The perturbation of a massless scalar field in the black hole’s background is adopted. The quasinormal modes are gotten by the 6th order WKB approximation approach and shadow radius, respectively. When the value of the Gauss–Bonnet coupling constant increase, the values of the real parts of the quasinormal modes increase and those of the imaginary parts decrease. The coincidence degrees of quasinormal modes derived by the two approaches increases with the increase of the values of the Gauss–Bonnet coupling constant and multipole number. It shows the correspondence between the shadow and test field in the four-dimensional Einstein–Gauss–Bonnet–Maxwell gravity. The radii of the photon sphere and shadow increase with the decrease of the Gauss–Bonnet coupling constant.

Eikonal quasinormal modes, photon sphere and shadow of a charged black hole in the 4D Einstein-Gauss-Bonnet gravity

“…The gravitational theory of EGB in D-dimensional spacetime coupled with an electromagnetic source is described by the action [46]…”

“…In particular, in the eikonal regime, the real and imaginary parts of QNMs frequencies for any spherically symmetric, asymptotically flat spacetime can be related to the frequency and instability time scale of unstable circular null geodesics. Therefore, in the eikonal limit, we can establish a correlation between the radius of the photon sphere R ps of a BH and its QNMs using the following analytical expression [4,45,46]…”

“…A recent work in [46] explored the correspondence between the shadow and the QNMs of the scalar field around a charged EGB 4D BH, using the 6 th order of the WKB method. In this work, we will extend the findings of this study by utilizing additional approaches and methods to explore the relationship between the photon sphere, the BH shadow, and the eikonal QNMs of scalar and electromagnetic field perturbations for a charged EGB 4D BH.…”

Charged black-bounce spacetimes: Photon rings, shadows and observational appearances

“…About two decades later, the image of the supermassive black hole located at the center of the Messier 87 galaxy (M87 * ) was announced [11][12][13][14][15][16] and further the first polarized images of this black hole were released [17] by the Event Horizon Telescope (EHT). These achievements are inspiring great attentions in studying [18][19][20][21][22][23][24][25][26][27][28][29][30][31] various aspects of the shadow and observational appearance of black holes.…”

Further clarification on quasinormal modes/circular null geodesics correspondence

“…Being unable to mention about 500 publications where this correspondence was discussed, we will review here only several most relevant contributions. Further development of the correspondence to black hole shadows and other configurations can be found in [8][9][10][11][12][13][14][15]. The case of axially symmetric black holes was discussed in [7] in the slow rotation regime, and further it was noticed that for Kerr black holes the correspondence between photon spheres and eikonal quaisnormal modes is more complicated for an arbitrary angular momentum [18].…”