论文标题
超越Schwarzschild-de保姆空间：iii。 $ r+r^2 $重力的非恒定标量曲率的扰动真空
Beyond Schwarzschild-de Sitter spacetimes: III. A perturbative vacuum with non-constant scalar curvature in $R+R^2$ gravity
论文作者
论文摘要
由于违反了尼尔森和其他人主张的广义Lichnerowicz Theorem，二次重力以非恒定标量曲率的态度接纳了真空吸尘器。在最近的出版物中[物理学。 Rev. d 106，104004（2022）]，我们振兴了一个Buchdahl的计划，该程序始于1962年，但过早地放弃了[Nuovo Cimento 23，141（1962）]，并发现了一类新颖的详尽阶层的静态球形，用于纯$ r^2 $ Grattity。我们在其中获得的Buchdahl启发的指标是表现出非恒定标量曲率的精确溶液。指标是四阶重力的产物，需要一个新的（buchdahl）参数$ k $，它允许RICCI标量在歧管上变化。指标能够通过避免对RICCI标量的渐近下降的过度限制来击败普遍的Lichnerowicz定理，如定理所假定。 buchdahl参数$ k $是纯$ r^2 $重力的新特征，这是一种更高衍生的理论。通过冒险，Buchdahl参数应该是整个更高衍生重力的通用标志，在本文中，我们试图将概念扩展到二次动作$ r^2+γ\，（R-2λ）$。我们能够确定二次场方程接收一个扰动真空，该真空有效期为$ o（k^2）$。 RICCI标量符合我们的指导直觉，包括渐变的案例，包括$ k \ neq0 $和$γ\ neq0 $。具有非恒定标量曲率的这种渐近平坦真空的存在使广义的Lichnerowicz Theorem完全击败。因此，我们的发现保证在完整的二次操作中恢复$ r^2 $项，$γ\，r+β\，r^2-α\，c^{μνρσ} c_ {μνρσ} $，在应用Lü-Perkins-Pope-pope-pope-stelle ansatz时。本文讨论了对Lü-Perkins-Pope-stelle解决方案的影响。
In violation of the generalized Lichnerowicz theorem advocated by Nelson and others, quadratic gravity admits vacua with non-constant scalar curvature. In a recent publication [Phys. Rev. D 106, 104004 (2022)], we revitalized a program that Buchdahl originated but prematurely abandoned circa 1962 [Nuovo Cimento 23, 141 (1962)], and uncovered a novel exhaustive class of static spherically symmetric vacua for pure $R^2$ gravity. The Buchdahl-inspired metrics we obtained therein are exact solutions which exhibit non-constant scalar curvature. A product of fourth-order gravity, the metrics entail a new (Buchdahl) parameter $k$ which allows the Ricci scalar to vary on the manifold. The metrics are able to defeat the generalized Lichnerowicz theorem by evading an overly strong restriction on the asymptotic falloff in the Ricci scalar as assumed in the theorem. The Buchdahl parameter $k$ is a new characteristic of pure $R^2$ gravity, a higher-derivative theory. By venturing that the Buchdahl parameter should be a universal hallmark of higher-derivative gravity at large, in this paper we seek to extend the concept to the quadratic action $R^2+γ\,(R-2Λ)$. We are able to determine that the quadratic field equation admits a perturbative vacuo that is valid up to the order $O(k^2)$. Conforming with our guiding intuition, the Ricci scalar is non-constant, including the asymptotically flat case, as long as $k\neq0$ and $γ\neq0$. The existence of such an asymptotically flat vacuo with non-constant scalar curvature defeats the generalized Lichnerowicz theorem in its entirety. Our finding thus warrants restoring the $R^2$ term in the full quadratic action, $γ\,R+β\,R^2-α\,C^{μνρσ}C_{μνρσ}$, when applying the Lü-Perkins-Pope-Stelle ansatz. Implications to the Lü-Perkins-Pope-Stelle solution are discussed herein.
