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On the renormalized volumes for conformally compact Einstein manifolds
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On the renormalized volumes for conformally compact Einstein manifolds
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We study the renormalized volume of a conformally compact Einstein manifold. In even dimensions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the dimension is odd, we relate the renormalized volume to the conformal primitive of the $Q$-curvature. We show how all the global information come from the Scattering.
Forward citations
Cited by 2 Pith papers
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Conformal Renormalisation of 8D Einstein Gravity
Holographic renormalisation of 8D Einstein-AdS gravity is recovered as the Einstein sector of the unique conformal gravity admitting constant-negative-curvature Einstein solutions, with matching counterterms.
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