A Bound on the Rate of Bondi Mass Loss

To ensure the light (emitted far away from the source of gravity) can arrive at the null infinity of an asymptotically flat spacetime, it is shown that the rate of Bondi mass aspect has to satisfy some conditions. In Einstein gravity theory, we find the sufficient condition implies a bound on the Bondi mass $m$, i.e., $|\dot{m}|\leqslant 0.3820~c^3/G$. This provides a new perspective on Dyson's maximum luminosity. However, in Brans-Dicke theory, the sufficient condition depends on the behavior of the radiation field of the scalar. Specifically, the photons can escape to the null infinity when the scalar gravitational radiation is not too large and the mass loss is not too fast.