L^2 curvature and volume renormalization of AHE metrics on 4-manifolds

Details L^2 curvature and volume renormalization of AHE metrics on 4-manifolds L^2 curvature and volume renormalization of AHE metrics on 4-manifolds

2000-11-08

arxiv.org/abs/math/0011051v2

Mathematics

Differential Geometry

15 pages, several corrections made. To appear in Math. Research Letters

Scientific paper

This paper relates the boundary term in the Chern-Gauss-Bonnet formula on 4-manifolds M with the renormalized volume V, as defined in the AdS/CFT correspondence, for asymptotically hyperbolic Einstein metrics on M. In addition, we compute and discuss the differential or variation dV of V, or equivalently the variation of the L^2 norm of the Weyl curvature, on the space of such Einstein metrics.

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