Curved spacetimes with continuous light disks

Highly curved spacetimes of compact astrophysical objects are known to possess light rings (null circular geodesics) with {\it discrete} radii on which massless particles can perform closed circular motions. In the present compact paper, we reveal for the first time the existence of isotropic curved spacetimes that possess light disks which are made of a {\it continuum} of closed light rings. In particular, using analytical techniques which are based on the non-linearly coupled Einstein-matter field equations, we prove that these physically intriguing spacetimes contain a central compact core of radius $r_{-}>0$ that supports an outer spherical shell with an infinite number (a continuum) of null circular geodesic which are all characterized by the functional relations $4\pi r_{\gamma }^{2}p(r_{\gamma })=1-3m(r_{\gamma })\mathrm{/}{r}_{\gamma }$ and $8\pi r_{\gamma }^2(\rho +p)=1$ for $r_{\gamma }\in [r_{-},r_{+}]$ [here $\{\rho ,p\}$ are respectively the energy density and the isotropic pressure of the self-gravitating matter fields and $m(r)$ is the gravitational mass contained within the sphere of radius $r$].