Formal power series for asymptotically hyperbolic Bach-flat metrics

Alaee, Aghil; Woolgar, Eric

doi:10.1007/s11005-020-01334-5

Cited by 3 publications

(7 citation statements)

References 20 publications

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“…While B ij is traceless for any d ≥ 4 and covariantly conserved for d = 4, it is not covariantly conserved for d > 4. However, the full expression for π ij (4) is conserved for any d (but not traceless for d > 4) and coincides with the modified Bach tensor introduced in [39]. Higher order terms in the iterative procedure produce analogues of the Bach tensor for higher dimensions that are more than quadratic in the curvatures.…”

Section: Recursion Relationsmentioning

confidence: 74%

Counterterms, Kounterterms, and the variational problem in AdS gravity

Anastasiou,

Miskovic,

Olea

et al. 2020

Preprint

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We show that the Kounterterms for pure AdS gravity in arbitrary even dimensions coincide with the boundary counterterms obtained through holographic renormalization if and only if the boundary Weyl tensor vanishes. In particular, the Kounterterms lead to a well posed variational problem for generic asymptotically locally AdS manifolds only in four dimensions. We determine the exact form of the counterterms for conformally flat boundaries and demonstrate that, in even dimensions, the Kounterterms take exactly the same form. This agreement can be understood as a consequence of Anderson's theorem for the renormalized volume of conformally compact Einstein 4-manifolds and its higher dimensional generalizations by Albin and Chang, Qing and Yang. For odd dimensional asymptotically locally AdS manifolds with a conformally flat boundary, the Kounterterms coincide with the boundary counterterms except for the logarithmic divergence associated with the holographic conformal anomaly, and finite local terms.

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Section: Recursion Relationsmentioning

confidence: 74%

Counterterms, Kounterterms, and the variational problem in AdS gravity

Anastasiou,

Miskovic,

Olea

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…As told above, unlike the Einstein gravity case, the coefficients g (2)ij and tr g (3)ij = g (3) remain undetermined by the Bach-flat condition [52]. However, the Penrose-Brown-Henneaux (PBH) transformations, which are valid for any AAdS spacetime regardless the EOM of the theory, keep the form of eqs.…”

Section: D Case Revisited: Einstein Gravity From Conformal Gravitymentioning

confidence: 97%

“…Eliminating the latter, they recovered the MacDowell-Mansouri action, what is an equivalent form of the renormalized Einstein-AdS action. In the same spirit, Alaee and Woolgar [52] determined the asymptotic expansion of Bach flat metrics in CG and provided the appropriate conditions needed to select the Einstein sector of the theory.…”

Section: D Case Revisited: Einstein Gravity From Conformal Gravitymentioning

confidence: 99%

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Einstein gravity from Conformal Gravity in 6D

Anastasiou

Araya

Olea

2021

J. High Energ. Phys.

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We extend Maldacena’s argument, namely, obtaining Einstein gravity from Conformal Gravity, to six dimensional manifolds. The proof relies on a particular combination of conformal (and topological) invariants, which makes manifest the fact that 6D Conformal Gravity admits an Einstein sector. Then, by taking generalized Neumann boundary conditions, the Conformal Gravity action reduces to the renormalized Einstein-AdS action. These restrictions are implied by the vanishing of the traceless Ricci tensor, which is the defining property of any Einstein spacetime. The equivalence between Conformal and Einstein gravity renders trivial the Einstein solutions of 6D Critical Gravity at the bicritical point.

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“…Eliminating the latter, they recovered the MacDowell-Mansouri action, what is an equivalent form of the renormalized Einstein-AdS action. In the same spirit, Alaee and Woolgar [51] determined the asymptotic expansion of Bach flat metrics in CG and provided the appropriate conditions needed to select the Einstein sector of the theory.…”

Section: D Case Revisited: Einstein Gravity From Conformal Gravitymentioning

confidence: 99%

Einstein Gravity from Conformal Gravity in 6D

Anastasiou,

Araya,

Olea

2020

Preprint

View full text Add to dashboard Cite

We extend Maldacena's argument, namely, obtaining Einstein gravity from Conformal Gravity, to six dimensional manifolds. The proof relies on a particular combination of conformal (and topological) invariants, which makes manifest the fact that 6D Conformal Gravity admits an Einstein sector. Then, by taking generalized Neumann boundary conditions, the Conformal Gravity action reduces to the renormalized Einstein-AdS action. These restrictions are implied by the vanishing of the traceless Ricci tensor, which is the defining property of any Einstein spacetime. The equivalence between Conformal and Einstein gravity renders trivial the Einstein solutions of 6D Critical Gravity at the bicritical point.

show abstract

Formal power series for asymptotically hyperbolic Bach-flat metrics

Cited by 3 publications

References 20 publications

Counterterms, Kounterterms, and the variational problem in AdS gravity

Counterterms, Kounterterms, and the variational problem in AdS gravity

Einstein gravity from Conformal Gravity in 6D

Einstein Gravity from Conformal Gravity in 6D

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