Optical behaviors of black holes in Starobinsky–Bel–Robinson gravity

Inspired by M-theory scenarios, we investigate optical properties of black holes in the Starobinsky–Bel–Robinsion gravity. Precisely, we study the shadows and the deflection angle of light rays by this class of black holes in such a novel gravity. First, we approach the shadows of the Schwarzschild-type solutions. As expected, we find perfect circular shadows where the size decreases with a stringy gravity parameter denoted by β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}. We reveal that this parameter is constrained by the shadow existence. Combining the Newman–Janis algorithm and the Hamilton–Jacobi mechanism, we examine the shadow behaviors of the rotating solutions in terms of one-dimensional real curves. Precisely, we obtain various sizes and shapes depending on the rotating parameter and the stringy gravity parameter a and β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}, respectively. To examine the shadow geometric deformations, we study the astronomical observables and the energy emission rate. As envisaged, we show that a and β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} have an impact on such shadow behaviors. For specific values of a, we remark that the obtained shadow shapes share certain similarities with the ones of the Kerr black holes in the plasma backgrounds. Using the Event Horizon Telescope observational data, we provide predictions for the stringy gravity parameter β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} which could play a relevant role in the M-theory compactifications. After that, we discuss the behaviors of the light rays near to such four dimensional black holes by calculating the deflection angle in terms of a required moduli space.