论文标题
带有共形耦合标量场的重力激
Gravitational instantons with conformally coupled scalar fields
论文作者
论文摘要
我们在麦克斯韦（Maxwell）和共同耦合标量场的存在下提出了新型的常规欧几里得解决方案，以实现一般相对论。特别是，我们考虑了Eguchi-Hanson和Taub-Nut家族的指标来分析求解场方程。这些解决方案具有我们明确计算的Hirzebruch Signature和Euler特征标记的非平凡拓扑。我们发现，尽管该解决方案与原始（反）自动二线eguchi-Hanson公制是本地不相等的，但它们的渐近局部欧几里得极限会导致相同的全球性质。我们重新审视先前在文献中发现的陶布坚固溶液，分析其坚果和螺栓结构，并获得重新归一化的欧几里得在壳上的作用以及它们的拓扑不变性。此外，我们讨论了如何在尊重共形不变性的高源性校正的情况下修改溶液。在形式不变的情况下，我们获得了新颖的Eguchi-Hanson和Taub-nut Solutions，并证明欧几里得在壳上的作用和Noether-Wald指控都是有限的，没有任何固有的边界对抗。
We present novel regular Euclidean solutions to General Relativity in presence of Maxwell and conformally coupled scalar fields. In particular, we consider metrics of the Eguchi-Hanson and Taub-NUT families to solve the field equations analytically. The solutions have nontrivial topology labeled by the Hirzebruch signature and Euler characteristic that we compute explicitly. We find that, although the solutions are locally inequivalent with the original (anti-)self-dual Eguchi-Hanson metric, their asymptotically locally Euclidean limit leads to the same global properties. We revisit the Taub-NUT solution previously found in the literature, analyze their nuts and bolts structure, and obtain the renormalized Euclidean on-shell action as well as their topological invariants. Additionally, we discuss how the solutions get modified in presence of higher-curvature corrections that respect conformal invariance. In the conformally invariant case, we obtain novel Eguchi-Hanson and Taub-NUT solutions and demonstrate that both Euclidean on-shell action and Noether-Wald charges are finite without any reference to intrinsic boundary counterterms.
