2020/06/30 by Zi-Chao Lin, Ke Yang, Shao-Wen Wei +2 · 1 citation
Physics and Astronomy · #Action (physics) #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #Equivalence (formal languages) #Field (mathematics) #Limit (mathematics) #Noncommutative and Quantum Gravity Theories #Regularization (linguistics) #Spacetime #String theory #Weak equivalence #gr-qc #hep-th
paper · pdf · doi:10.1140/epjc/s10052-020-08612-5
published as Eur. Phys. J. C 80, 1033 (2020) · 20 pages, 9 figures, published version
openalex publication_date 2020/11/01 · arxiv created 2020/11/18 · arxiv updated 2020/11/19 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
Abstract Recently, a novel four-dimensional Einstein–Gauss–Bonnet (EGB) theory was presented to bypass the Lovelock’s theorem and to give nontrivial effects on the four-dimensional local gravity. The main mechanism is to introduce a redefinition α → α /(D-4) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>→</mml:mo> <mml:mi>α</mml:mi> <mml:mo>/</mml:mo> <mml:mo>(</mml:mo> <mml:mi>D</mml:mi> <mml:mo>-</mml:mo> <mml:mn>4</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and to take the limit D→ 4 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>→</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> . However, this theory does not have standard four-dimensional field equations. Some regularization procedures are then proposed to address this problem ( http://arxiv.org/abs/2003.11552 , http://arxiv.org/abs/2003.12771 , http://arxiv.org/abs/2004.08362 , http://arxiv.org/abs/2004.09472 , http://arxiv.org/abs/2004.10716 ). The resultant regularized four-dimensional EGB theory has the same on-shell action as the original theory. Thus it is expected that the novel four-dimensional EGB theory is equivalent to its regularized version. However, the equivalence of these two theories is symmetry-dependent. In this paper, we test the equivalence in a cylindrically symmetric spacetime. The well-defined field equations of the two theories are obtained, with which our follow-up analysis shows that they are equivalent in such spacetime. Cylindrical cosmic strings are then considered as specific examples of the metric. Three sets of solutions are obtained and the corresponding string mass densities are evaluated. The results reveal how the Gauss–Bonnet term in four dimensions contributes to the string geometry in the new theory.