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 $r_{\gamma}^{in}\leqslant \frac{12}{5}M$, where $r_{\gamma}^{in}$ is the radius of the innermost photonsphere and $M$ is the total ADM mass of the asymptotically flat compact star spacetime.