Positive energy theorem for (4+1)-dimensional asymptotically anti-de Sitter spacetimes

We define the total energy-momenta for (4+1)-dimensional asymptotically anti-de Sitter spacetimes, which comes from the boundary terms at infinity in the integral form of the Weitzenbock formula. Then we prove the positive energy theorem for such spacetimes, following Witten’s original arguments for the positive energy theorem in asymptotically flat spacetimes.