紧双星系统Binding Energy的引力自力修正

Second-order self-force calculation of the gravitational binding energy in compact binaries

Self-force theory is the leading method of modeling extreme-mass-ratio inspirals (EMRIs), key sources for the gravitational-wave detector LISA. It is well known that for an accurate EMRI model, second-order self-force effects are critical, but calculations of these effects have been beset by obstacles. In this letter we present the first implementation of a complete scheme for second-order self-force computations, specialized to the case of quasicircular orbits about a Schwarzschild black hole. As a demonstration, we calculate the gravitational binding energy of these binaries.

后牛顿binding energy和引力波通量中有效高阶项的估算：非自旋致密双星内旋

Estimating effective higher order terms in the post-Newtonian binding energy and gravitational-wave flux: Non-spinning compact binary inspiral

在绝热后牛顿（PN）近似下，通过将束缚能的变化与引力波（引力波）通量等效，计算了准圆轨道上螺旋形致密双星的引力波相位演化.该能量平衡方程可以以不同的方式求解，这导致PN波形的多个近似。由于PN展开的收敛性差，这些近似值在螺旋后期往往彼此不同。这些近似应该被选择作为模板的GWs的检测和参数估计的吸入紧凑的二进制是不明显的。在本文中，我们提出了有效的高阶（超出目前可用的4PN和3.5PN）非自旋项的PN扩展的结合能和GW通量，最大限度地减少多个PN近似（泰勒T1，泰勒T2，泰勒T4，泰勒F2）与有效的一个身体波形校准到数值相对论（EOBNR）的差异的估计。我们发现，PN近似使用有效的高阶项构建显示出显着更好的协议（相比3.5PN）与螺旋部分的EOBNR。对于非自旋双星与组件质量$m_{1,2} \in [1.4 M_\odot, 15 M_\odot]$，大多数的近似有一个匹配（忠实度）的EOBNR和彼此超过99%。

Assessing the Energetics of Spinning Binary Black Hole Systems

In this work we study the dynamics of spinning binary black hole systems in the strong field regime. For this purpose we extract from numerical relativity simulations the binding energy, specific orbital angular momentum, and gauge-invariant orbital frequency. The goal of our work is threefold: First, we extract the individual spin contributions to the binding energy, in particular the spin-orbit, spin-spin, and cubic-in-spin terms. Second, we compare our results with predictions from waveform models and find that while post-Newtonian approximants are not capable of representing the dynamics d…

Gravitational waves from spinning binary black holes at the leading post-Newtonian orders at all orders in spin

We determine the binding energy, the total gravitational wave energy flux, and the gravitational wave modes for a binary of rapidly spinning black holes, working in linearized gravity and at leading orders in the orbital velocity, but to all orders in the black holes' spins. Though the spins are treated nonperturbatively, surprisingly, the binding energy and the flux are given by simple analytical expressions which are finite (respectively third- and fifth-order) polynomials in the spins. Our final results are restricted to the important case of quasi-circular orbits with the black holes' spin…

The Lamb shift and the gravitational binding energy for binary black holes

We show that the correction to the gravitational binding energy for binary black holes due to the tail effect resembles the Lamb shift in the Hydrogen atom. In both cases a 'conservative' effect arises from interactions with 'radiation' modes, and moreover an explicit cancelation between near and far zone divergences is at work. In addition, regularization scheme-dependence may introduce ambiguity parameters. This is remediated, within an effective field theory approach, by the implementation of the zero-bin subtraction. We illustrate the procedure explicitly for the Lamb shift, by performing …

广义相对论和后牛顿理论下的双黑洞力学第一定律

The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory

黑洞力学或热力学的第一定律有各种不同的形式。本文从纯后牛顿（PN）分析出发，得到了点质量双星系统沿正圆轨道运动的第一定律。我们的计算是有效的，通过3PN阶，并包括，此外，在4PN和5PN阶的对数项的贡献。这个二元点粒子力学的第一定律，然后从广义相对论的第一性原理推导出来，并与单个和二元黑洞的情况进行类比。PN时空的第一定律的一些后果进行了探讨。作为一个这样的结果，一个简单的关系PN的结合能的二元系统和Detweiler的红移观测之间的建立。通过它，我们能够高精度地确定一些以前未知的高阶PN系数的数值在圆轨道结合能。最后，我们提出了新的规范不变的概念的能量和角动量的粒子在一个二元系统。