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).A preprint version of the article is available at ArXiv.

中文翻译：

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4D爱因斯坦-高斯-引擎盖引力中的Born-Infeld黑洞

Glavan和Lin（Phys。Rev. Lett。124：081301，2020）提出了一种新颖的四维爱因斯坦-高斯-贝内特引力，其目的是绕过洛夫洛克定理，并对这四个定理做出不平凡的贡献维引力动力学。然而，该理论的有效性和一致性最近受到质疑。我们研究了在新颖的四维爱因斯坦-高斯-贝内特引力下由伯恩-英费尔德电场充电的静态和球对称黑洞。已经发现，由于从无限远处入射的粒子可以达到奇点，所以黑洞解决方案仍然遭受奇点问题。还证明，在这种新的引力理论中，Born-Infeld带电黑洞可能优于Maxwell带电黑洞，这是类似Schwarzschild-AdS的黑洞的带电扩展。还分析了黑洞解决方案的一些基本热力学。此外，我们在Lü和Pang（arXiv：2003.11552）提出的正则化四维Einstein-Gauss-Bonnet引力中重新获得黑洞解。该文章的预印本可从ArXiv获得。