Lower-dimensional Limits of Cubic Lovelock Gravity

Abstract

In this paper, we obtain the lower-dimensional limits $(p=2,3,4,5,6)$ of cubic Lovelock gravity through a regularized Kaluza-Klein reduction. By taking a flat internal space for simplicity, we also study the static black hole solutions in the resulting theories. We show that the solutions match with the ones obtained from the "naive limit" of $D$-dimensional equation for the metric function, which is obtained by first scaling the relevant couplings by a factor of $\frac{1}{D-p}$ and then taking the limit $D\to p$, with one important exception: In 4D, one obtains the expected solution only for the black hole with a planar horizon.

arXiv comment11 pages + appendix; v2: minor corrections, references added; v3: introduction and section 2 improved, more references and a link to Mathematica files added; v4: Title changed, introduction and last section revised, version to appear in Nuclear Physics B; v5: 2 references about Lovelock black holes added, minor typo in the expression for black hole temperature on page 4 corrected

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• Regular BTZ black holes from an infinite tower of corrections
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• 3D Lovelock Gravity and the Holographic c-Theorem
• Microscopic entropy of static black holes in 3d Lovelock gravities
• Scaling symmetry, Smarr relation, and the extended first law in lower-dimensional Lovelock gravity
• AdS${}_3$ black holes with primary Proca hair from a regularized Gauss-Bonnet coupling
• Regular AdS${}_3$ black holes from regularized Gauss-Bonnet coupling