Does photon capture in a black hole (or any other "very compact" object) reduce the luminosity/photon flux from its self isotropic emission?
Let's answer the question from the point of view of a stable neutron star.
The luminosity is
$$L_0 = 4\pi R_0^2 \sigma T_{0}^4$$
in the inertial frame of the neutron star surface (assume a non-spinning object).
For a distant observer, the radius of the neutron star is (e.g. see Haensel 2001)
$$R_{\infty}= R_0 \left(1 - R_s/R_0\right)^{-1/2}\, ,$$
the temperature is
$$T_{\infty} = T_0 \left(1 - R_s/R_0\right)^{1/2}\ ,$$
and the luminosity
$$L_{\infty} = L_0\left(1 - R_s/R_0\right)\ .$$
$R_s$ is the usual Schwarzschild radius.
I think the fact that $L_{\infty} &lt; L_0$ is the effect you are talking about.