The Physics Society of Iran Iranian Journal of Physics Research 1682-6957 26 1 2026 05 22 Photon sphere and shadow of dynamical Kottler black hole Photon sphere and shadow of dynamical Kottler black hole 55 60 3789 10.47176/ijpr.26.1.92192 FA Zahra Allahyari Jalali Tarbiat Modares University Ali Akbar Asgari Tarbiat Modares University Journal Article 2025 09 23 <span>In this paper, we analyze the shadow of a black hole immersed in a dynamic background reflecting the expansion of the universe due to the presence of dark energy. Using a time-dependent metric (the dynamic Kottler metric), we obtain the null (lightlike) geodesics of spacetime and calculate the effective potential for light rays. Our results show that the expansion of the universe causes the radius of the photon sphere, and consequently the black hole shadow, to decrease gradually over time. This phenomenon can be a way to determine cosmological parameters.</span> <span>In this paper, we analyze the shadow of a black hole immersed in a dynamic background reflecting the expansion of the universe due to the presence of dark energy. Using a time-dependent metric (the dynamic Kottler metric), we obtain the null (lightlike) geodesics of spacetime and calculate the effective potential for light rays. Our results show that the expansion of the universe causes the radius of the photon sphere, and consequently the black hole shadow, to decrease gradually over time. This phenomenon can be a way to determine cosmological parameters.</span> https://ijpr.iut.ac.ir/article_3789_335d3d1cd7ef05ec77714a215134914c.pdf