Energy-momentum for Randall-Sundrum models

The conservation law of energy-momentum (or the definition of energy-momentum density) for the gravitational field is one of the most fundamental and controversial problems in general relativity. As a true field, it would be natural to expect that gravity should has its own local energy-momentum density. However, it is usually asserted that such a density can not be locally defined because of the equivalence principle.1 As a consequence, many attempts to identify an energy-momentum density for the gravitational field lead to complexes that are not true tensors. The first of such attempt was made by Einstein who proposed an expression for the energymomentum density of the gravitational field. Bauer and Shrödinger 2,3 pointed out