On the maximally symmetric vacua of generic Lovelock gravities
arXiv:2408.08094 · doi:10.1088/1751-8121/ad9cd6
Abstract
We survey elementary features of Lovelock gravity and its maximally symmetric vacuum solutions. The latter is solely determined by the real roots of a dimension-dependent polynomial. We also recover the static spherically symmetric (black hole) solutions of Lovelock gravity using Palais' symmetric criticality principle. We show how to linearize the generic field equations of Lovelock models about a given maximally symmetric vacuum, which turns out to factorize into the product of yet another dimension-dependent polynomial and the linearized Einstein tensor about the relevant background. We also describe how to compute conserved charges using linearized field equations along with the relevant background Killing isometries. We further describe and discuss the special vacua which are defined by the simultaneous vanishing of the aforementioned polynomials.
arXiv commentprepared as a contribution to the special issue of "Journal of Physics A: Mathematical and Theoretical" dedicated to the memory of Stanley Deser; 20 pages, no figures; version 2: references added, 21 pages; version 3: improved with new calculations in Section 3 and Appendix B, 22 pages; version 4: matches the accepted copy with 4 new references
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