  We highlight here the fact that the distantly observed luminosity of a
spherically symmetric compact star radiating thermal radiation isotropically is
higher by a factor of $(1+z_{\rm b})^2$ compared to the corresponding flat
space-time case, where $z_{\rm b}$ is the surface gravitational redshift of the
compact star. In particular, we emphasize that if the thermal radiation is
indeed emitted isotropically along the respective normal directions at each
point, this factor of increment $(1+z_{\rm b})^2$ remains unchanged even if the
compact object would lie within its {\em photon sphere}. Since a canonical
neutron star has $z_{\rm b} \approx 0.1$, the actual X-ray luminosity from the
neutron star surface could be $\sim 20 \%$ higher than what would be
interpreted by ignoring the general relativistic effects described here. For a
static compact object, supported by only isotropic pressure, compactness is
limited by the Buchdahl limit $z_{\rm b} < 2.0$. However, for compact objects
supported by anisotropic pressure, $z_{\rm b}$ could be even higher ($z_{\rm b}
< 5.211$). In addition, in principle, there could be ultra-compact objects
having $z_{\rm b} \gg 1$. Accordingly, the general relativistic effects
described here might be quite important for studies of thermal radiation from
some ultra-compact objects.
