by both black-hole and naked-singularity types of the external R-N spacetime (for details see [@Kot-Stu-Tor:2008:CLASQG:]).

In the standard ($b = 0$) internal Schwarzschild spacetimes of uniform energy density [@Schw:1916:SITBA:; @Stu:2000:ACTPS2:] with radius $R < 3GM/c^2$, bound null geodesics exist being concentrated around the stable circular null geodesic [@Abr-Mil-Stu:1993:PHYSR4:; @Stu-etal:2001:PHYSR4:]. From the behaviour of the effective potential of null geodesics in the exterior, vacuum Schwarzschild spacetimes, determining the unstable null circular geodesics at the radius $r_{\mathrm{ph}} = 3GM/c^2$ (see, e.g., [@Mis-Tho-Whe:1973:Gra:]), we can conclude that any spherically symmetric, static non-singular interior spacetime with radius $R < r_{\mathrm{ph}}$ admits existence of bound null geodesics. The trapped null geodesics are then governed by both internal and external barriers of the null geodesics effective potential. [^1] The realistic equations of state admitting the existence of the extremely compact objects were found and investigated for neutron stars, quark stars and Q-stars [@Bah-Lyn-Sel:1990:ApJ:; @Mil-Sha-Nol:1998:MNRAS:; @Nil-Cla:2000:GRRelStarsPolyEOS:; @Stu-Tor-Hle-Urb:2009:; @Hle-Stu-Mra:2004:RAGtime4and5:CrossRef; @Oest:2001:RAGtime2and3:]. For spacetimes with a non-zero tidal charge, the situation is more complex as we shall demonstrate in the following.

The existence of bound null geodesics in ECS has interesting astrophysical consequences. For example, using the notion of the optical reference geometry [@Abr-Pra:1990:; @Stu-Hle-Jur:2000:; @Stu:1990:] it was shown that 