A note on the novel 4D Einstein–Gauss–Bonnet gravity

By Wen-Yuan Ai. Communications in Theoretical Physics, 2020

180 citations recorded by the source corpus.

Recently, a novel 4D Einstein–Gauss–Bonnet gravity has been proposed by Glavan and Lin (2020 Phys. Rev. Lett. 124 081301) by rescaling the coupling α → α / ( D − 4 ) and taking the limit D → 4 at the level of equations of motion. This prescription, though was shown to bring non-trivial effects for some spacetimes with particular symmetries, remains mysterious and calls for scrutiny. Indeed, there is no continuous way to take the limit D → 4 in the higher D-dimensional equations of motion because the tensor indices depend on the spacetime dimension and behave discretely. On the other hand, if one works with 4D spacetime indices the contribution corresponding to the Gauss–Bonnet term vanishes identically in the equations of motion. A necessary condition (but may not be sufficient) for this procedure to work is that there is an embedding of the 4D spacetime into the higher D-dimensional spacetime so that the equations in the latter can be properly interpreted after taking the limit. In this note, working with 2D Einstein gravity, we show several subtleties when applying the method used in (2020 Phys. Rev. Lett. 124 081301).

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c6bdd0c788c7581e0ffd5ad4380248c168f0ce16

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Citations in the corpus

Derivation of regularized field equations for the Einstein-Gauss-Bonnet theory in four dimensions (2020, methodology): “We remark that the regularized theory of [45] admits exactly the same solutions as R = T gravity in 2D [12, 40, 59], but that it also admits a finite and well-defined action.”
On taking the D → 4 limit of Gauss-Bonnet gravity: theory and solutions (2020, background): “(2)This approach was recently ‘rediscovered’ [26, 39] in considering generalization of the D = 4 Gauss–Bonnet solutions.”
A consistent theory of D → 4 Einstein-Gauss-Bonnet gravity (2020, background): “On the other hand, in [12] it was shown at the level of equations of motion that a diffeomorphism invariant theory cannot be realized (see also [13–15]).”
Innermost stable circular orbit and shadow of the 4D Einstein–Gauss–Bonnet black hole (2020, result): “As we mentioned in the introduction, the above limiting procedure has been called into question by subsequent works [9–15].”