Abstract
We establish the inequality for Henneaux–Teitelboim's total energy–momentum for asymptotically anti-de Sitter initial data sets which are asymptotic to arbitrary t-slice in anti-de Sitter spacetime. In particular, when t = 0, it generalizes Chruściel–Maerten–Tod's inequality in the center of AdS mass coordinates. We also show that the determinant of energy–momentum endomorphism Q is the geometric invariant of asymptotically anti-de Sitter spacetimes.
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