论文标题
超越Schwarzschild-de保姆空间：II。纯$ r^{2} $重力和$ r^{2} $ spaceTimes的新的异常属性中的确切的非SCHWARZSCHILD度量
Beyond Schwarzschild-de Sitter spacetimes: II. An exact non-Schwarzschild metric in pure $R^{2}$ gravity and new anomalous properties of $R^{2}$ spacetimes
论文作者
论文摘要
在我们最近的出版物（物理学修订版106，104004（2022））中，我们提出了一个布奇达尔（Buchdahl）起源但过早放弃的计划（Nuovo Cimento Cimento 23，141（1962））。在其中，我们获得了一类详尽的指标，这些指标构成了Vacuo中纯$ r^{2} $字段方程的非平凡解决方案的分支。通常，布赫达尔启发的指标通常具有非恒定标量曲率，从而击败了先前主张的二次引力的广义Lichnerowicz Theorem。我们发现，所述定理对RICCI标量的空间衍生物的渐近下降做出了过于强烈的假设，使其对Buchdahl启发的指标违反。在本文中，我们将进一步扩展上述工作，以表明在Buchdahl启发的指标类别中，渐近平坦的成员采用精确的封闭分析表达。新指标的特征是地平线半径$ r _ {\ text {s}} $和buchdahl参数$ k $，后者通过$ r^{2} $ dravity的高衍生性质出现。对于$ k = 0 $，新公制恢复了经典的Schwarzschild公制。配备了新指标的精确表达式，我们应分析构建纯$ r^{2} $ spacetime的kruskal-szekeres图。我们发现，buchdahl参数$ k $从根本上修改了$ r^{2} $时空结构的属性。
In our recent publication (Phys. Rev. D 106, 104004 (2022)), we advanced a program that Buchdahl originated but prematurely abandoned circa 1962 (Nuovo Cimento 23, 141 (1962)). Therein we obtained an exhaustive class of metrics that constitute the branch of non-trivial solutions to the pure $R^{2}$ field equation in vacuo. The Buchdahl-inspired metrics in general possess non-constant scalar curvature, thereby defeating the generalized Lichnerowicz theorem previously advocated for quadratic gravity. We found that the said theorem makes an overly strong assumption on the asymptotic falloff in the spatial derivatives of the Ricci scalar, rendering it violable against the Buchdahl-inspired metrics. In this paper, we shall further extend our work mentioned above by showing that, within the class of Buchdahl-inspired metrics, the asymptotically flat member takes on an exact closed analytical expression. The new metric is characterized by a horizon radius $r_{\text{s}}$ and the Buchdahl parameter $k$, the latter of which arises via the higher-derivative nature of $R^{2}$ gravity. For $k=0$, the new metric recovers the classic Schwarzschild metric. Equipped with the exact expression of the new metric, we shall analytically construct the Kruskal-Szekeres diagram for pure $R^{2}$ spacetime. We find that the Buchdahl parameter $k$ fundamentally modifies the properties of $R^{2}$ spacetime structures in a variety of ways.
