Outer boundary conditions for Einstein's field equations in harmonic coordinates
Milton Ruiz, Oliver Rinne, Olivier Sarbach
备注：
Added more details on specifying initial data and the numerical calculation of reflection coefficients. 24 pages, 11 figures. To appear in Classical and Quantum Gravity
We analyze Einstein's vacuum field equations in generalized harmonic coordinates on a compact spatial domain with boundaries. We specify a class of boundary conditions which is constraint-preserving and sufficiently general to include recent proposals for reducing the amount of spurious reflections of gravitational radiation. In particular, our class comprises the boundary conditions recently proposed by Kreiss and Winicour, a geometric modification thereof, the freezing-Psi0 boundary condition and the hierarchy of absorbing boundary conditions introduced by Buchman and Sarbach. Using the recent technique developed by Kreiss and Winicour based on an appropriate reduction to a pseudo-differential first order system, we prove well posedness of the resulting initial-boundary value problem in the frozen coefficient approximation. In view of the theory of pseudo-differential operators it is expected that the full nonlinear problem is also well posed. Furthermore, we implement some of our boundary conditions numerically and study their effectiveness in a test problem consisting of a perturbed Schwarzschild black hole.
Third post-Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic-coordinate and ADM-Hamiltonian formalisms
Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order in harmonic coordinates
Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, CNRS, Université PSL, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室）；University of Southampton（南安普顿大学）
Constructing the canonical harmonic coordinates of Kerr metric to the fourth post-Minkowskian order
School of Physics and Astronomy, Beijing Normal University（北京师范大学物理学院）；School of Mathematics and Statistics, and Hunan Provincial University Key Laboratory for Big Data Analysis and Application, Hunan First Normal University（湖南第一师范学院数学与统计学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础物理与数学科学学院）
Multipole Expansion of Gravitational Waves: from Harmonic to Bondi coordinates
我们将多极后闵可夫斯基近似中孤立物质源的度规从简谐（de Donder）坐标变换到辐射Newman-Unti（NU）坐标。为了线性化的顺序，我们得到的NU度规作为源的质量和电流多极矩的功能，有效的整个外部区域的源。施加适当的边界条件，我们恢复广义Bondi-van der Burg-Metzner-Sachs剩余对称群。对于二次阶，在质量-四极相互作用的情况下，我们确定了引力波尾在NU度规中的贡献，并证明了度规的半径展开对所有阶都是正则的.质量和角动量方面，以及邦迪剪切，从公制读出。它们由包括尾项的辐射四极矩给出。
