Maximum Accretion Efficiency in General Theory of Relativity

We derive here the expression for the accretion luminosity, $L(\mathrm{\infty })$, as seen by a distant inertial observer $S_{\mathrm{\infty }}$, for the case of spherical accretion onto a static compact object having a surface gravitational red-shift $z_x$. It is found that the ``efficiency’’ for conversion of mass energy into accretion energy is given by $ϵ=z_x\mathrm{/}(1+z_x)$. And since the maximum value of $z_x$ permitted by General Theory of Relativity (GTR) is 2, the maximum theoretical value of the accretion efficiency is 66.66%.