Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-01-07
Phys.Rev. D71 (2005) 084009
Physics
High Energy Physics
High Energy Physics - Theory
12 pages, no figure, submitted to Phys. Rev. D. v2: minor corrections, refs. added
Scientific paper
10.1103/PhysRevD.71.084009
We consider $n$-dimensional asymptotically anti-de Sitter spacetimes in higher curvature gravitational theories with $n \geq 4$, by employing the conformal completion technique. We first argue that a condition on the Ricci tensor should be supplemented to define an asymptotically anti-de Sitter spacetime in higher curvature gravitational theories and propose an alternative definition of an asymptotically anti-de Sitter spacetime. Based on that definition, we then derive a conservation law of the gravitational field and construct conserved quantities in two classes of higher curvature gravitational theories. We also show that these conserved quantities satisfy a balance equation in the same sense as in Einstein gravity and that they reproduce the results derived elsewhere. These conserved quantities are shown to be expressed as an integral of the electric part of the Weyl tensor alone and hence they vanish identically in the pure anti-de Sitter spacetime as in the case of Einstein gravity.
Koga Jun-ichirou
Okuyama Naoya
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