Upper bound on the radius of the innermost photonsphere in the regular compact star spacetime

Abstract

We study properties of the innermost photonsphere in the regular compact star background. We take the traceless energy–momentum tensor and dominant energy conditions. In the regular compact star background, we analytically obtain an upper bound on the radius of the innermost photonsphere as rγin⩽125M,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{\\gamma }^{in}\\leqslant \\frac{12}{5}M,$$\\end{document} where rγin\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{\\gamma }^{in}$$\\end{document} is the radius of the innermost photonsphere and M is the total ADM mass of the asymptotically flat compact star spacetime.