Horndeski gravity as D → 4 limit of Gauss-Bonnet

By Hsueh-I Lu, Y. Pang. 2020

274 citations recorded by the source corpus.

We propose a procedure for the $D\rightarrow 4$ limit of Einstein-Gauss-Bonnet (EGB) gravity that leads to a well defined action principle in four dimensions. Our construction is based on compactifying $D$-dimensional EGB gravity on a $(D-4)$-dimensional maximally symmetric space followed by redefining the Gauss-Bonnet coupling $\alpha\rightarrow \frac{\alpha}{D-4}$. The resulting model is a special scalar-tensor theory that belongs to the family of Horndeski gravity. Static black hole solutions in the scalar-tensor theory are investigated. Interestingly, the metric profile is independent of the curvature of the internal space and coincides with the $D\rightarrow 4$ limit of the usual EGB black hole with the unusual Gauss-Bonnet coupling $\frac{\alpha}{D-4}$. The curvature information of the internal space is instead encoded in the profile of the extra scalar field. Our procedure can also be generalized to define further limits of the Gauss-Bonnet combination by compactifying the $D$-dimensional theory on a $(D-p)$-dimensional maximally symmetric space with $p\leq 3$. These lead to different $D\rightarrow 4$ limits of EGB gravity as well as its $D\rightarrow 2,3$ limits.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1ed737cd00c36440a38910d10acb4e2be3556c50

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Citations in the corpus

Shadows and photon spheres with spherical accretions in the four-dimensional Gauss–Bonnet black hole (2020, background): “Many characteristics of the four-dimensional Gauss-Bonnet black hole have been investigated [23, 24, 25, 26, 27, 28, 29, 30, 31, 32].”
The 4D Einstein–Gauss–Bonnet theory of gravity: a review (2022, methodology): “For the theory resultant from the Kaluza–Klein regularization scheme, we have a solution again given by the metric function (116) with q = Q2 for the scalar field profile number (2) in equation (118) (with β = 2λα) [201].”
Rotating black holes in 4D Einstein-Gauss-Bonnet gravity and its shadow (2020, methodology): “6) emerges as a solution of the 4D regularized theories [51, 52, 58].”
A consistent theory of D → 4 Einstein-Gauss-Bonnet gravity (2020, background): “1), and the resultant D → 4 EGB gravity has a scalar dof as shown by [4, 5, 10].”
A note on the novel 4D Einstein–Gauss–Bonnet gravity (2020, background): “additional fields in the effective four-dimensional theory [52].”
Innermost stable circular orbit and shadow of the 4D Einstein–Gauss–Bonnet black hole (2020, methodology): “For example, [16,17] considered using the Kaluza–Klein approach of the D → 4 limit to obtain a well-defined theory that belongs to the Horndeski class [18].”
Effective scalar-tensor description of regularized Lovelock gravity in four dimensions (2020, methodology): “[24] H. Lu and Y. Pang, Horndeski Gravity as D → 4 Limit of Gauss-Bonnet, 2003.11552.”
On taking the D → 4 limit of Gauss-Bonnet gravity: theory and solutions (2020, methodology): “It was argued in [27] that this is not a problem because the scalar field does not appear alone in the action.”
Extended thermodynamics and microstructures of four-dimensional charged Gauss-Bonnet black hole in AdS space (2020, methodology): “Note that this entropy is the same as that obtained from the Iyer-Wald formula [38].”
Derivation of regularized field equations for the Einstein-Gauss-Bonnet theory in four dimensions (2020, methodology): “[10, 11] that the cosmological and black hole solutions found in the original paper on novel 4DEGB gravity [9] are also solutions of the field equations derived from the action (27).”