On taking the D → 4 limit of Gauss-Bonnet gravity: theory and solutions

By Robie A. Hennigar, D. Kubizňák, Robert B. Mann, Christopher Pollack. 2020

212 citations recorded by the source corpus.

We comment on the recently introduced Gauss-Bonnet gravity in four dimensions. We argue that it does not make sense to consider this theory to be defined by a set of D → 4 solutions of the higher-dimensional Gauss-Bonnet gravity. We show that a well-defined D → 4 limit of Gauss-Bonnet Gravity is obtained generalizing a method employed by Mann and Ross to obtain a limit of the Einstein gravity in D = 2 dimensions. This is a scalar-tensor theory of the Horndeski type obtained by dimensional reduction methods. By considering simple spacetimes beyond spherical symmetry (Taub-NUT spaces) we show that the naive limit of the higher-dimensional theory to D = 4 is not well defined and contrast the resultant metrics with the actual solutions of the new theory.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e3295df8537e7e329fba6cc66b7b24417ad99bb3

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Citations in the corpus

Effective scalar-tensor description of regularized Lovelock gravity in four dimensions (2020, unknown): “After the first version of this paper was submitted, it was pointed out that the same scalar-tensor theory (with K = 0) is obtained also by introducing a counter term to the action to cancel the divergence in the D → 4 limit [24, 25].”
A consistent theory of D → 4 Einstein-Gauss-Bonnet gravity (2020, background): “The same results are deduced in [7, 8] (see also [9]) by adding a counter term in Ddimensions and then taking the D → 4 limit.”
Regular Black Holes From Pure Gravity (2024, unknown): “Yet, it may be possible to embed our solutions in four dimensions by taking the D → 4 limit of the corresponding Quasi-topological action analogously to the D → 4 limit of Gauss-Bonnet gravity [64–67].”
Shadows and photon spheres with spherical accretions in the four-dimensional Gauss–Bonnet black hole (2020, background): “Recently, there are also some authors [42, 43, 44, 45] to point out that this theory is not well-defined.”
Rotating black holes in 4D Einstein-Gauss-Bonnet gravity and its shadow (2020, background): “6) emerges as a solution of the 4D regularized theories [51, 52, 58].”
The 4D Einstein–Gauss–Bonnet theory of gravity: a review (2022, unknown): “These have resulted in novel scalar–tensor theories either via a conformal regularization [203, 204] (first applied in reference [58] in two-dimensions), or via a regularized Kaluza–Klein reduction [201, 202].”
A note on the novel 4D Einstein–Gauss–Bonnet gravity (2020, unknown): “[73–79].”
Innermost stable circular orbit and shadow of the 4D Einstein–Gauss–Bonnet black hole (2020, background): “The same theory can also be deduced by introducing a counter term into the action [19,20].”
Gravitational lensing by black holes in the 4D Einstein-Gauss-Bonnet gravity (2020, background): “Furthermore, the static spherically symmetric 4D black hole solution found in [10, 33] remains valid for these alternate regularised theories [15, 19, 34, 41].”