Positivity of the Bondi mass in Bondi's radiating spacetimes
  We find two conditions related to the {\it news functions} of the Bondi's radiating vacuum spacetimes. We provide a complete proof of the positivity of the Bondi mass by using Schoen-Yau's method under one condition and by using Witten's method under another condition. 
Wen-ling Huang, Shing Tung Yau, Xiao Zhang