extremely compact stars (ECS). The parameter space $(b-R)$ is separated into five Zones I–IV${}_\mathrm{a, b}$; their properties are given in Section \[SECngaep\].[]{data-label="FIGzone"}](Fig1.pdf){width="0.8\hsize"}

Extremely compact neutron stars
-------------------------------

The ECS (neutron, quark, or hybrid) are defined by the existence of trapped null geodesics in the interior of the compact star. In the case of internal uniform density Schwarzschild spacetimes ($b = 0$), such objects appear just when the surface of the compact star is located under the photon circular geodesic of the external vacuum Schwarzschild spacetime located at $r_\mathrm{ph} = 3r_\mathrm{g}$ [@Stu-Tor-Hle-Urb:2009:]. In the braneworld uniform density compact stars this simple rule does not hold and the situation is more complex due to different character of the external spacetime and its relation to the internal spacetime.

Assuming the external spacetime to be of the Reissner-Nordström (R-N) type with the tidal charge substituting the electric charge squared appearing in the standard R-N spacetimes, the photon circular geodesics are given by the condition $$r^2 - 3r_\mathrm{g}r + 2q = 0.$$

However, it is convenient to use dimensionless tidal charge $b$ and dimensionless radial coordinate defined by $$r/r_\mathrm{g}\rightarrow r.$$

For negative tidal charges ($b < 0$) external spacetimes of the black-hole type are allowed 