How can one observe gravitational angular momentum radiation from a dynamical source near null infinity?

To answer a question of how can one observed angular momentum radiation near null infinity, one can first transform the dynamical twisting vacuum solution and make it satisfy Bondi coordinate conditions in the asymptotical region of the null infinity. We then obtain the Bondi-Sachs news function and also find the relationship of how does the angular momentum contribute to the news functions from the exact solution sense. By using the Komar's integral of angular momentum, the gravitational angular momentum flux of the dynamical twisting space-time can be obtained. All of our results can be compared with the Kerr solution, Robbinson-Trautmann or Schwarzschild solution. This study can provide a theoretical basis to understand the correlations of gravitational radiations near a rotating dynamical horizon and null infinity.