Thermal Radiation from Compact Objects in Curved Space-Time
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.