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2014

Local Well-posedness of Lovelock gravity

Willison, Steven

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It has long been known that Lovelock gravity, being of Cauchy-Kowalevskaya type, admits a well defined initial value problem for analytic data.

However, this does not address the physically important issues of continuous dependence of the solution on the data and the domain of dependence property.
In this note we fill this gap in our understanding of the (local) dynamics of the theory.
We show that, by a known mathematical trick, the fully nonlinear harmonic-gauge-reduced Lovelock field equations can be made equivalent to a quasilinear PDE system.

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Similar

Q. Han and J. Hong, “Isometric Embedding of Riemannian Manifolds in Euclidean Spaces,” Mathematical surveys and monographs, AMS (2006)
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E. Gravanis and S. Willison, Phys. Rev. D 75
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For a recent review and bibliography see T. Padmanabhan and D. Kothawala, Phys. Rept. 531
Original
2013
Cited alongside, same era.
H. Reall, N. Tanahashi and B. Way, “Causality and Hyperbolicity of Lovelock Theories,” arXiv:1406.3379 [hep-th]
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H. S. Reall, N. Tanahashi and B. Way, “Shock Formation in Lovelock Theories,” arXiv:1409.3874 [hep-th]
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Cited in the paper.
M. A. Ramirez, arXiv:1207.6810 [gr-qc]
Original
Cited in the paper.

Then

G. Kunstatter, T. Taves and H. Maeda, Class. Quant. Grav. 29
Original
2013
Later among the works it cites.
K. Izumi, “Causal Structures in Gauss-Bonnet gravity,” Phys. Rev. D 90
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2014
Closest in time.

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