Mechanics of extended masses in general relativity
Mechanics of extended masses in general relativity
复制标题
广义相对论中扩展质量的力学
DOI：
--
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Abraham I. Harte
中科院分区：
文献类型：
--
作者：
Abraham I. Harte
广义相对论研究的是扩展物体的“外部”或“整体”运动。只要不与其他应力能量源直接（非重力）接触，就允许具有基本上任意形状、自旋、内部成分和速度的致密物质物体。物理上合理的线动量和角动量提出了这样的机构和精确的方程描述其演变。动量的变化取决于某种“有效度量”，这与最初在自作用力文献中引入的Detweiler-Whiting R-场的非微扰推广密切相关。如果一个自引力体内部的有效度量可以通过适当的幂级数来适当地近似，则施加在其上的瞬时重力和扭矩被示出为与施加在以有效度量移动的适当测试体上的力和扭矩相同。这个结果适用于所有的多极阶。物体自场的唯一瞬时效应是使其应力-能量张量的“裸”多极矩重新正规化。作为一个简单的应用程序恢复的MisaTaQuWa表达式的引力自。还得到了重力自转矩。最后，它表明，有效的度量，其中物体似乎移动是近似的解决方案，真空爱因斯坦方程的物理度量是一个近似的解决方案，爱因斯坦方程线性化的真空背景。
The ‘external’ or ‘bulk’ motion of extended bodies is studied in general relativity. Compact material objects of essentially arbitrary shape, spin, internal composition and velocity are allowed as long as there is no direct (non-gravitational) contact with other sources of stress–energy. Physically reasonable linear and angular momenta are proposed for such bodies and exact equations describing their evolution are derived. Changes in the momenta depend on a certain ‘effective metric’ that is closely related to a non-perturbative generalization of the Detweiler–Whiting R-field originally introduced in the self-force literature. If the effective metric inside a self-gravitating body can be adequately approximated by an appropriate power series, the instantaneous gravitational force and torque exerted on it is shown to be identical to the force and torque exerted on an appropriate test body moving in the effective metric. This result holds to all multipole orders. The only instantaneous effect of a body’s self-field is to finitely renormalize the ‘bare’ multipole moments of its stress–energy tensor. The MiSaTaQuWa expression for the gravitational self-force is recovered as a simple application. A gravitational self-torque is obtained as well. Lastly, it is shown that the effective metric in which objects appear to move is approximately a solution to the vacuum Einstein equation if the physical metric is an approximate solution to Einstein’s equation linearized about a vacuum background.