Shadows of a generic class of spherically symmetric, static spacetimes

We explore the characteristics of shadows for a general class of spherically symmetric, static spacetimes, which may arise in general relativity or in modified theories of gravity. The chosen line element involves a sum (with constant but different coefficients) of integer powers of 1r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{\text {r}}$$\end{document} in gtt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {g}_{\text {tt}}$$\end{document} and grr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {g}_{\text {rr}}$$\end{document}, in the Schwarzschild gauge. We begin our discussion by motivating the line element through a study of the energy conditions (null and weak) and the extent to which they are satisfied/violated for diverse choices of the parameters appearing in the metric functions. Subsequently, we construct the circular shadows and analyse the dependence of the shadow radius on the metric parameters. We find that with specific choices of the metric parameters (within the ranges allowed by the energy conditions) one can, in principle, obtain values that conform with recent observations on shadows, as available in the literature. We also mention where such metrics may arise (i.e. in which theory of gravity and the physical scenario therein), thereby proposing that the observed shadows may be representative signatures of different theoretical contexts.