论文标题
引力波从二次重力中的灵感黑洞引起
Gravitational waves from inspiraling black holes in quadratic gravity
论文作者
论文摘要
我们在二次引力的背景下通过灵感黑洞发出的引力波研究。通过在平坦背景周围的场方程线性线程，我们证明了所有自由度都满足了波浪状的方程。这些自由度分为三种模式：一种巨大的旋转 - $ 2 $模式，巨大的旋转 - $ 0 $模式和预期的无质量旋转$ 2 $模式。我们构建了引力波的能量量张量，并表明，由于巨大的旋转$ 2 $模式，它呈现了Ostrogragradski的不稳定性。我们还展示了如何处理这种可能的病理并为系统获得一致的物理解释。使用能量弹药张量，我们研究了每个巨大模式在轨道动力学中的影响，并将其与一般相对性的标准结果进行了比较。此外，我们提出了两种约束与大量旋转$ 2 $贡献相关的参数$α$的方法。从第一个方法，使用旋转$ 2 $模式的组合波形，我们获得约束$α\ lyssim 1.1 \ times 10^{21} m^{2} $。在第二种方法中，使用聚结时间，我们获得约束$α\ Lessim 1.1 \ times 10^{13} m^{2} $。
We peform a study of gravitational waves emitted by inspiraling black holes in the context of quadratic gravity. By linearizing the field equations around a flat background, we demonstrate that all degrees of freedom satisfy wave-like equations. These degrees of freedom split into three modes: a massive spin-$2$ mode, a massive spin-$0$ mode, and the expected massless spin-$2$ mode. We construct the energy-momentum tensor of gravitational waves and show that, due to the massive spin-$2$ mode, it presents the Ostrogradski instability. We also show how to deal with this possible pathology and obtain consistent physical interpretations for the system. Using the energy-momentum tensor, we study the influence of each massive mode in the orbital dynamics and compare it with the standard result of General Relativity. Moreover, we present two methods to constrain the parameter $α$ associated with the massive spin-$2$ contribution. From the first method, using the combined waveform for the spin-$2$ modes, we obtain the constraint $ α\lesssim 1.1 \times 10^{21} m^{2}$. In the second method, using the coalescence time, we get the constraint $ α\lesssim 1.1 \times 10^{13} m^{2}$.
