A note on the total action of 4D Gauss–Bonnet theory

Mahapatra, Subhash

doi:10.1140/epjc/s10052-020-08568-6

“…However, the original claim of ref. [37] is clearly in contradiction with the Lovelock theorem, and some subtleties and criticisms on the D → 4 limit were revealed in [87][88][89][90][91], concluding that there is no pure four-dimensional Einstein-Gauss-Bonnet gravity [92,93]. In refs.…”

Section: Jhep12(2020)192mentioning

confidence: 99%

Holographic superconductors in 4D Einstein-Gauss-Bonnet gravity

Qiao

¹

,

Ouyang

²

,

Wang

³

et al. 2020

J. High Energ. Phys.

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We investigate the neutral AdS black-hole solution in the consistent D → 4 Einstein-Gauss-Bonnet gravity proposed in [K. Aoki, M.A. Gorji, and S. Mukohyama, Phys. Lett. B810 (2020) 135843] and construct the gravity duals of (2 + 1)-dimensional superconductors with Gauss-Bonnet corrections in the probe limit. We find that the curvature correction has a more subtle effect on the scalar condensates in the s-wave superconductor in (2 + 1)-dimensions, which is different from the finding in the higher-dimensional superconductors that the higher curvature correction makes the scalar hair more difficult to be developed in the full parameter space. However, in the p-wave case, we observe that the higher curvature correction always makes it harder for the vector condensates to form in various dimensions. Moreover, we note that the higher curvature correction results in the larger deviation from the expected relation in the gap frequency ωg/Tc ≈ 8 in both (2 + 1)-dimensional s-wave and p-wave models.

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“…This processing method in [41] has led to a great deal of discussion, see e.g. [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60].…”

Section: Introductionmentioning

confidence: 99%

Hawking evaporation of Einstein–Gauss–Bonnet AdS black holes in $$D\geqslant 4$$ dimensions

Wu

¹

,

Hu

²

,

Xu

³

2021

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Einstein–Gauss–Bonnet theory is a string-generated gravity theory when approaching the low energy limit. By introducing the higher order curvature terms, this theory is supposed to help to solve the black hole singularity problem. In this work, we investigate the evaporation of the static spherically symmetric neutral AdS black holes in Einstein–Gauss–Bonnet gravity in various spacetime dimensions with both positive and negative coupling constant $$\alpha $$ α . By summarizing the asymptotic behavior of the evaporation process, we find the lifetime of the black holes is dimensional dependent. For $$\alpha >0$$ α > 0 , in $$D\geqslant 6$$ D ⩾ 6 cases, the black holes will be completely evaporated in a finite time, which resembles the Schwarzschild-AdS case in Einstein gravity. While in $$D=4,5$$ D = 4 , 5 cases, the black hole lifetime is always infinite, which means the black hole becomes a remnant in the late time. Remarkably, the cases of $$\alpha >0, D=4,5$$ α > 0 , D = 4 , 5 will solve the terminal temperature divergent problem of the Schwarzschild-AdS case. For $$\alpha <0$$ α < 0 , in all dimensions, the black hole will always spend a finite time to a minimal mass corresponding to the smallest horizon radius $$r_{min}=\sqrt{2|\alpha |}$$ r min = 2 | α | which coincide with an additional singularity. This implies that there may exist constraint conditions to the choice of coupling constant.

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“…However, there are also some debates on whether the novel gravity is a consistent and well-defined theory in four dimensions [45][46][47][48][49][50][51][52][53]. Such as, Gurses et al pointed out that the novel 4D EGB gravity does not admit a description in terms of a covariantly-conserved rank-2 tensor in four dimensions and the dimensional regularization procedure is ill-defined, since one part of the GB tensor, the Lanczos-Bach tensor, always remains higher dimensional [46].…”

Section: Introductionmentioning

confidence: 99%

“…So generally speaking, the theory only makes sense on some selected highly-symmetric spacetimes, such as the FLRW spacetime and static spherically symmetric spacetime. Mahapatra found that in the limiting D → 4 procedure, the theory gives unphysical divergences in the on-shell action and surface terms in four dimensions [47]. Shu showed that at least the vacuum of the theory is either unphysical or unstable, or has no well-defined limit as D → 4 [48].…”

Section: Introductionmentioning

confidence: 99%

Born–Infeld black holes in 4D Einstein–Gauss–Bonnet gravity

Yang

¹

,

Gu

²

,

Wei

³

et al. 2020

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A novel four-dimensional Einstein-Gauss-Bonnet gravity was formulated by Glavan and Lin (Phys. Rev. Lett. 124:081301, 2020), which is intended to bypass the Lovelock’s theorem and to yield a non-trivial contribution to the four-dimensional gravitational dynamics. However, the validity and consistency of this theory has been called into question recently. We study a static and spherically symmetric black hole charged by a Born–Infeld electric field in the novel four-dimensional Einstein–Gauss–Bonnet gravity. It is found that the black hole solution still suffers the singularity problem, since particles incident from infinity can reach the singularity. It is also demonstrated that the Born-Infeld charged black hole may be superior to the Maxwell charged black hole to be a charged extension of the Schwarzschild-AdS-like black hole in this new gravitational theory. Some basic thermodynamics of the black hole solution is also analyzed. Besides, we regain the black hole solution in the regularized four-dimensional Einstein–Gauss–Bonnet gravity proposed by Lü and Pang (arXiv:2003.11552).

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A note on the total action of 4D Gauss–Bonnet theory

Cited by 113 publications

References 34 publications

Holographic superconductors in 4D Einstein-Gauss-Bonnet gravity

Holographic superconductors in 4D Einstein-Gauss-Bonnet gravity

Hawking evaporation of Einstein–Gauss–Bonnet AdS black holes in $$D\geqslant 4$$ dimensions

Born–Infeld black holes in 4D Einstein–Gauss–Bonnet gravity

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