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Accurate calculation of gravitational wave memory

Gravitational wave memory is an important prediction of general relativity. The detection of the gravitational wave memory can be used to test general relativity and deduce the property of the gravitational wave source. A quantitative model is important for such detection and signal interpretation. Previous works on gravitational wave memory have always used the energy flux of the gravitational wave to calculate the memory. Accurately calculating the memory is highly demanded. Here we apply the Bondi-Metzner-Sachs method to calculate the gravitational wave memory. Our method does not need slow motion and weak field conditions for the gravitational wave source. This method can accurately calculate the memory if the nonmemory waveform is known. As an example, we combine our method with the matured numerical relativity result of a nonmemory waveform for binary black hole coalescence. We calculate the waveform for the memory which can be used to aid memory detection and help us understand the gravitational wave source. Our calculation result is consistent with the numerical relativity result of memory. We determine the dependence of the memory amplitude on the mass ratio and the spins of the two spin-aligned black holes.